As a frequently-observed phenomenon in the northern South China Sea(nSCS),subsurface chlorophyll maximum(SCM)evolution from summer to winter remains unclear,neither the associated hydrographic control.In this study,on...As a frequently-observed phenomenon in the northern South China Sea(nSCS),subsurface chlorophyll maximum(SCM)evolution from summer to winter remains unclear,neither the associated hydrographic control.In this study,on the basis of in-situ data of fall-season cruises in 2004–2006,we characterized the depth,thickness and intensity of the SCM in the nSCS using a general Gaussian-function fitting approach,and investigated a linkage to the corresponding ocean vertical buoyance properties.Our results show that the SCM becomes deeper,thicker and less intense offshore-wards in the nSCS during fall seasons.In parallel,a correlation between the SCM variation and mixed layer depth exists in the nSCS,and it becomes pronounced in the shelf region compared to the slope and basin areas in autumn.Physically,once warmer surface ocean and thus stronger thermo-determined stratification,the SCM layer goes deeper and becomes thicker and less intense in the nSCS,especially in the shelf area of the nSCS.Moreover,the impact of water temperatures at deeper layers on the vertical stratification exerts more consequent roles on the spatial variability of SCM,compared to surface temperatures in the nSCS.Specifically,the isotherm line of 22℃ acts as crucial indicator for variations of the SCM in the nSCS during autumns.展开更多
This study investigates the Maximum Power Point Tracking(MPPT)control method of offshore windphotovoltaic hybrid power generation system with offshore crane-assisted.A new algorithm of Global Fast Integral Sliding Mod...This study investigates the Maximum Power Point Tracking(MPPT)control method of offshore windphotovoltaic hybrid power generation system with offshore crane-assisted.A new algorithm of Global Fast Integral Sliding Mode Control(GFISMC)is proposed based on the tip speed ratio method and sliding mode control.The algorithm uses fast integral sliding mode surface and fuzzy fast switching control items to ensure that the offshore wind power generation system can track the maximum power point quickly and with low jitter.An offshore wind power generation system model is presented to verify the algorithm effect.An offshore off-grid wind-solar hybrid power generation systemis built in MATLAB/Simulink.Compared with other MPPT algorithms,this study has specific quantitative improvements in terms of convergence speed,tracking accuracy or computational efficiency.Finally,the improved algorithm is further analyzed and carried out by using Yuankuan Energy’s ModelingTech semi-physical simulation platform.The results verify the feasibility and effectiveness of the improved algorithm in the offshore wind-solar hybrid power generation system.展开更多
The present study was carried out in order to track the maximum power point in a variable speed turbine by minimizing electromechanical torque changes using a sliding mode control strategy. In this strategy, first, th...The present study was carried out in order to track the maximum power point in a variable speed turbine by minimizing electromechanical torque changes using a sliding mode control strategy. In this strategy, first, the rotor speed is set at an optimal point for different wind speeds. As a result of which, the tip speed ratio reaches an optimal point, mechanical power coefficient is maximized, and wind turbine produces its maximum power and mechanical torque. Then, the maximum mechanical torque is tracked using electromechanical torque. In this technique, tracking error integral of maximum mechanical torque, the error, and the derivative of error are used as state variables. During changes in wind speed, sliding mode control is designed to absorb the maximum energy from the wind and minimize the response time of maximum power point tracking(MPPT). In this method, the actual control input signal is formed from a second order integral operation of the original sliding mode control input signal. The result of the second order integral in this model includes control signal integrity, full chattering attenuation, and prevention from large fluctuations in the power generator output. The simulation results, calculated by using MATLAB/m-file software, have shown the effectiveness of the proposed control strategy for wind energy systems based on the permanent magnet synchronous generator(PMSG).展开更多
A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where ...A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.展开更多
In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be descr...In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and L^vy processes （AFBSDEDLs）, we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs＇ preliminary result with certain classical convex variational techniques, the corresponding maxi- mum principle is proved.展开更多
This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables...This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem.展开更多
When the wind speed changes significantly in a permanent magnet synchronous wind power generation system,the maximum power point cannot be easily determined in a timely manner.This study proposes a maximum power refer...When the wind speed changes significantly in a permanent magnet synchronous wind power generation system,the maximum power point cannot be easily determined in a timely manner.This study proposes a maximum power reference signal search method based on fuzzy control,which is an improvement to the climbing search method.A neural network-based parameter regulator is proposed to address external wind speed fluctuations,where the parameters of a proportional-integral controller is adjusted to accurately monitor the maximum power point under different wind speed conditions.Finally,the effectiveness of this method is verified via Simulink simulation.展开更多
The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but t...The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but the control domain is not necessarily convex.展开更多
A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary an...A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps.展开更多
The advantage of fuzzy controllers in working with inaccurate and nonlinear inputs is that there is no need for an accurate mathematical model and fast convergence and minimal fluctuations in the maximum power point d...The advantage of fuzzy controllers in working with inaccurate and nonlinear inputs is that there is no need for an accurate mathematical model and fast convergence and minimal fluctuations in the maximum power point detector.The capability of online fuzzy tracking systems is maximum power,resistance to radiation and temperature changes,and no need for external sensors to measure radiation intensity and temperature.However,the most important issue is the constant changes in the amount of sunlight that cause the maximum power point to be constantly changing.The controller used in the maximum power point tracking(MPPT)circuit must be able to adapt to the new radiation conditions.Therefore,in this paper,to more accurately track the maximumpower point of the solar system and receive more electrical power at its output,an adaptive fuzzy control was proposed,the parameters of which are optimized by the whale algorithm.The studies have repeated under different irradiation conditions and the proposed controller performance has been compared with perturb and observe algorithm(P&O)method,which is a practical and high-performance method.To evaluate the performance of the proposed algorithm,the particle swarm algorithm optimized the adaptive fuzzy controller.The simulation results show that the adaptive fuzzy control system performs better than the P&O tracking system.Higher accuracy and consequently more production power at the output of the solar panel is one of the salient features of the proposed control method,which distinguishes it from other methods.On the other hand,the adaptive fuzzy controller optimized by the whale algorithm has been able to perform relatively better than the controller designed by the particle swarm algorithm,which confirms the higher accuracy of the proposed algorithm.展开更多
This study proposes a fuzzy system for tracking the maximum power point of a PV system for solar panel. The solar panel and maximum power point tracker have been modeled using MATLAB/Simulink. A simulation model consi...This study proposes a fuzzy system for tracking the maximum power point of a PV system for solar panel. The solar panel and maximum power point tracker have been modeled using MATLAB/Simulink. A simulation model consists of PV panel, boost converter, and maximum power point tack MPPT algorithm is developed. Three different conditions are simulated: 1) Uniform irradiation;2) Sudden changing;3) Partial shading. Results showed that fuzzy controller successfully find MPP for all different weather conditions studied. FLC has excellent ability to track MPP in less than 0.01 second when PV is subjected to sudden changes and partial shading in irradiation.展开更多
In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwi...In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward Stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.展开更多
This paper presents the implementation of maximum power point tracking （MPPT） with fuzzy logic controller. For cost consideration, an inexpensive 8-bit microcontroller, PIC 16F877A, is selected and programmed with C...This paper presents the implementation of maximum power point tracking （MPPT） with fuzzy logic controller. For cost consideration, an inexpensive 8-bit microcontroller, PIC 16F877A, is selected and programmed with C language and integer variables For evaluation, the implemented fuzzy logic controller （FLC） is compared with the MPPT controller of using perturbation and observation （P＆O）. Both types of MPPT controllers are tested on the same voltage source with a series-connected resistor. Experimental results show that the implemented FLC with appropriate design meets the control requirements of MPPT. The FLC based on linguistic fuzzy rules has more flexibility and intelligence than conventional P＆O controller, but the FLC spends more RAM and ROM spaces than the P＆O tracker does.展开更多
Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This r...Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This review synthesizes the theoretical advancements,computational approaches,emerging challenges,and possible research directions in the field.Firstly,we briefly review the fundamental theory of continuous-time optimal control,including Pontryagin's maximum principle(PMP)and dynamic programming principle(DPP).Secondly,we present the foundational results in optimal impulse control,including necessary conditions and sufficient conditions.Thirdly,we systematize impulse game methodologies,from Nash equilibrium existence theory to the connection between Nash equilibrium and systems stability.Fourthly,we summarize the numerical algorithms including the intelligent computation approaches.Finally,we examine the new trends and challenges in theory and applications as well as computational considerations.展开更多
Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for dela...Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for delay-independent stability and delay-dependent stability of singular networked control systems are derived and transformed to a feasibility problem of linear matrix inequality formulation, which can be solved by the Matlab LMI toolbox, and the feasible solutions provide the maximum allowable delay bound that makes the system stable. A numerical example is provided, which shows that the analysis method is valid and the stability criteria are feasible.展开更多
基金Supported by the Ministry of Science and Technology of the People’s Republic of China(No.2019 YFE 0125000)the National Natural Science Foundation of China-Shandong Joint Fund(No.U 1906215)+1 种基金the National Natural Science Foundation of China(No.41406010)partially by the Key Laboratory of Coastal Environmental Processes and Ecological Remediation,Chinese Academy of Sciences Opening Fund(No.2020 KFJJ 04)。
文摘As a frequently-observed phenomenon in the northern South China Sea(nSCS),subsurface chlorophyll maximum(SCM)evolution from summer to winter remains unclear,neither the associated hydrographic control.In this study,on the basis of in-situ data of fall-season cruises in 2004–2006,we characterized the depth,thickness and intensity of the SCM in the nSCS using a general Gaussian-function fitting approach,and investigated a linkage to the corresponding ocean vertical buoyance properties.Our results show that the SCM becomes deeper,thicker and less intense offshore-wards in the nSCS during fall seasons.In parallel,a correlation between the SCM variation and mixed layer depth exists in the nSCS,and it becomes pronounced in the shelf region compared to the slope and basin areas in autumn.Physically,once warmer surface ocean and thus stronger thermo-determined stratification,the SCM layer goes deeper and becomes thicker and less intense in the nSCS,especially in the shelf area of the nSCS.Moreover,the impact of water temperatures at deeper layers on the vertical stratification exerts more consequent roles on the spatial variability of SCM,compared to surface temperatures in the nSCS.Specifically,the isotherm line of 22℃ acts as crucial indicator for variations of the SCM in the nSCS during autumns.
基金supported by the 2022 Sanya Science and Technology Innovation Project,China(No.2022KJCX03)the Sanya Science and Education Innovation Park,Wuhan University of Technology,China(Grant No.2022KF0028)the Hainan Provincial Joint Project of Sanya Yazhou Bay Science and Technology City,China(Grant No.2021JJLH0036).
文摘This study investigates the Maximum Power Point Tracking(MPPT)control method of offshore windphotovoltaic hybrid power generation system with offshore crane-assisted.A new algorithm of Global Fast Integral Sliding Mode Control(GFISMC)is proposed based on the tip speed ratio method and sliding mode control.The algorithm uses fast integral sliding mode surface and fuzzy fast switching control items to ensure that the offshore wind power generation system can track the maximum power point quickly and with low jitter.An offshore wind power generation system model is presented to verify the algorithm effect.An offshore off-grid wind-solar hybrid power generation systemis built in MATLAB/Simulink.Compared with other MPPT algorithms,this study has specific quantitative improvements in terms of convergence speed,tracking accuracy or computational efficiency.Finally,the improved algorithm is further analyzed and carried out by using Yuankuan Energy’s ModelingTech semi-physical simulation platform.The results verify the feasibility and effectiveness of the improved algorithm in the offshore wind-solar hybrid power generation system.
文摘The present study was carried out in order to track the maximum power point in a variable speed turbine by minimizing electromechanical torque changes using a sliding mode control strategy. In this strategy, first, the rotor speed is set at an optimal point for different wind speeds. As a result of which, the tip speed ratio reaches an optimal point, mechanical power coefficient is maximized, and wind turbine produces its maximum power and mechanical torque. Then, the maximum mechanical torque is tracked using electromechanical torque. In this technique, tracking error integral of maximum mechanical torque, the error, and the derivative of error are used as state variables. During changes in wind speed, sliding mode control is designed to absorb the maximum energy from the wind and minimize the response time of maximum power point tracking(MPPT). In this method, the actual control input signal is formed from a second order integral operation of the original sliding mode control input signal. The result of the second order integral in this model includes control signal integrity, full chattering attenuation, and prevention from large fluctuations in the power generator output. The simulation results, calculated by using MATLAB/m-file software, have shown the effectiveness of the proposed control strategy for wind energy systems based on the permanent magnet synchronous generator(PMSG).
基金supported by the National Natural Science Foundation of China(61203129,61174038,61473151,51507080)the Fundamental Research Funds for the Central Universities(30915011104,30920130121010,30920140112005)
基金supported by the National Basic Research Program of China (973 Program, 2007CB814904)the National Natural Science Foundations of China (10921101)+2 种基金Shandong Province (2008BS01024, ZR2010AQ004)the Science Funds for Distinguished Young Scholars of Shandong Province (JQ200801)Shandong University (2009JQ004),the Independent Innovation Foundations of Shandong University (IIFSDU,2009TS036, 2010TS060)
文摘A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.
基金Supported by the National Natural Science Foundation(11221061 and 61174092)111 project(B12023),the National Science Fund for Distinguished Young Scholars of China(11125102)Youth Foundation of QiLu Normal Institute(2012L1010)
文摘In this paper, we study the stochastic maximum principle for optimal control prob- lem of anticipated forward-backward system with delay and Lovy processes as the random dis- turbance. This control system can be described by the anticipated forward-backward stochastic differential equations with delay and L^vy processes （AFBSDEDLs）, we first obtain the existence and uniqueness theorem of adapted solutions for AFBSDEDLs; combining the AFBSDEDLs＇ preliminary result with certain classical convex variational techniques, the corresponding maxi- mum principle is proved.
基金supported by the National Natural Science Foundation of China(11701214)Shandong Provincial Natural Science Foundation,China(ZR2019MA045).
文摘This paper is concerned with a Pontryagin's maximum principle for the stochastic optimal control problem with distributed delays given by integrals of not necessarily linear functions of state or control variables.By virtue of the duality method and the generalized anticipated backward stochastic differential equations,we establish a necessary maximum principle and a sufficient verification theorem.In particular,we deal with the controlled stochastic system where the distributed delays enter both the state and the control.To explain the theoretical results,we apply them to a dynamic advertising problem.
基金supported partially by the National Natural Science Foundation of China under Grant 61503348the Hubei Provincial Natural Science Foundation of China under Grant 2015CFA010the 111 project under Grant B17040
文摘When the wind speed changes significantly in a permanent magnet synchronous wind power generation system,the maximum power point cannot be easily determined in a timely manner.This study proposes a maximum power reference signal search method based on fuzzy control,which is an improvement to the climbing search method.A neural network-based parameter regulator is proposed to address external wind speed fluctuations,where the parameters of a proportional-integral controller is adjusted to accurately monitor the maximum power point under different wind speed conditions.Finally,the effectiveness of this method is verified via Simulink simulation.
基金Supported by National Natural Science Foundation of P.R.China (10371067) the Youth Teacher Foundation of Fok Ying Tung Education Foundation (91064)New Century Excellent Young Teachers Foundation of P. R. China (NCEF-04-0633)
文摘The maximum principle for fully coupled forward-backward stochastic control system in the global form is proved, under the assumption that the forward diffusion coefficient does not contain the control variable, but the control domain is not necessarily convex.
基金supported by the Doctoral foundation of University of Jinan(XBS1213)the National Natural Science Foundation of China(11101242)
文摘A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps.
文摘The advantage of fuzzy controllers in working with inaccurate and nonlinear inputs is that there is no need for an accurate mathematical model and fast convergence and minimal fluctuations in the maximum power point detector.The capability of online fuzzy tracking systems is maximum power,resistance to radiation and temperature changes,and no need for external sensors to measure radiation intensity and temperature.However,the most important issue is the constant changes in the amount of sunlight that cause the maximum power point to be constantly changing.The controller used in the maximum power point tracking(MPPT)circuit must be able to adapt to the new radiation conditions.Therefore,in this paper,to more accurately track the maximumpower point of the solar system and receive more electrical power at its output,an adaptive fuzzy control was proposed,the parameters of which are optimized by the whale algorithm.The studies have repeated under different irradiation conditions and the proposed controller performance has been compared with perturb and observe algorithm(P&O)method,which is a practical and high-performance method.To evaluate the performance of the proposed algorithm,the particle swarm algorithm optimized the adaptive fuzzy controller.The simulation results show that the adaptive fuzzy control system performs better than the P&O tracking system.Higher accuracy and consequently more production power at the output of the solar panel is one of the salient features of the proposed control method,which distinguishes it from other methods.On the other hand,the adaptive fuzzy controller optimized by the whale algorithm has been able to perform relatively better than the controller designed by the particle swarm algorithm,which confirms the higher accuracy of the proposed algorithm.
文摘This study proposes a fuzzy system for tracking the maximum power point of a PV system for solar panel. The solar panel and maximum power point tracker have been modeled using MATLAB/Simulink. A simulation model consists of PV panel, boost converter, and maximum power point tack MPPT algorithm is developed. Three different conditions are simulated: 1) Uniform irradiation;2) Sudden changing;3) Partial shading. Results showed that fuzzy controller successfully find MPP for all different weather conditions studied. FLC has excellent ability to track MPP in less than 0.01 second when PV is subjected to sudden changes and partial shading in irradiation.
文摘In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward Stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.
文摘This paper presents the implementation of maximum power point tracking （MPPT） with fuzzy logic controller. For cost consideration, an inexpensive 8-bit microcontroller, PIC 16F877A, is selected and programmed with C language and integer variables For evaluation, the implemented fuzzy logic controller （FLC） is compared with the MPPT controller of using perturbation and observation （P＆O）. Both types of MPPT controllers are tested on the same voltage source with a series-connected resistor. Experimental results show that the implemented FLC with appropriate design meets the control requirements of MPPT. The FLC based on linguistic fuzzy rules has more flexibility and intelligence than conventional P＆O controller, but the FLC spends more RAM and ROM spaces than the P＆O tracker does.
基金Supported by National Natural Science Foundation of China （10671112）, National Basic Research Program of China （973 Program） （2007CB814904）, the Natural Science Foundation of Shandong Province （Z2006A01）, and the Chinese New Century Young Teachers Program The authors would like to thank the referees for a careful reading of this paper and helpful suggestions which made the revised version more readable.
文摘Optimal impulse control and impulse games provide the cutting-edge frameworks for modeling systems where control actions occur at discrete time points,and optimizing objectives under discontinuous interventions.This review synthesizes the theoretical advancements,computational approaches,emerging challenges,and possible research directions in the field.Firstly,we briefly review the fundamental theory of continuous-time optimal control,including Pontryagin's maximum principle(PMP)and dynamic programming principle(DPP).Secondly,we present the foundational results in optimal impulse control,including necessary conditions and sufficient conditions.Thirdly,we systematize impulse game methodologies,from Nash equilibrium existence theory to the connection between Nash equilibrium and systems stability.Fourthly,we summarize the numerical algorithms including the intelligent computation approaches.Finally,we examine the new trends and challenges in theory and applications as well as computational considerations.
基金the National Natural Science Foundation of China (60574011)the National Natural Science Foundation of Liaoning Province (2050770).
文摘Based on bounded network-induced time-delay, the networked control system is modeled as a linear time-variant singular system. Using the Lyapunov theory and the linear matrix inequality approach, the criteria for delay-independent stability and delay-dependent stability of singular networked control systems are derived and transformed to a feasibility problem of linear matrix inequality formulation, which can be solved by the Matlab LMI toolbox, and the feasible solutions provide the maximum allowable delay bound that makes the system stable. A numerical example is provided, which shows that the analysis method is valid and the stability criteria are feasible.
