Analysis And Synthesis Of High-order Stochastic Nonlinear Systems With Output Constraints

Stochastic models can well describe dynamic systems,and it is one of the hot topics in the nonlinear system field in recent years.However,many complex dynamic systems are difficultly modeled by strict-feedback stochastic nonlinear systems.The high-order stochastic nonlinear system contains the exponential terms,which can describe the dynamic characteristic in the inherent nonlinear systems.Therefore,the high-order stochastic nonlinear system becomes one of the effective models to solve the modeling problems of complex systems.The Jacobian linearization of such system may not exist or is null and uncontrollable,which causes that it is very difficult to study the control problem of such a kind of systems.Thus,high-order stochastic nonlinear systems have become a new research topic and attracted more attentions.However,the existing research on high-order stochastic nonlinear systems mainly focuses on the control design without any constraints.To our best knowledge,due to the consideration of system performance,production safety and lifes of physical device,many real systems are usually subject to output constraints.The requirement will aggravate the nonlinearities,which results in that the existing control schemes are no longer applicable.Therefore,the research on the control design of high-order stochastic nonlinear systems with output constraints has important theoretical value and practical significance.Based on above background,this paper is aimed to investigate the control problem of high-order stochastic nonlinear systems with symmetric and asymmetric output constraints.To deal with these output constraint issues,some new barrier Lyapunov functions(BLFs)are proposed in this paper.Combining the proposed BLFs and the adding a power integrator technique,some control schemes are developed.The designed state feedback controller can guarantee the closed-loop system is finite-time stable or bounded in probability of without violating the given output constraints.The main research contents and innovations of the dissertation are listed as follows:(1)For high-order stochastic nonlinear systems with special structure and output constraints,a BLF-based control scheme is proposed.Firstly,a novel tan-type BLF with higher-order and flexible form is constructed by taking full advantage of the information of growth conditions.Secondly,by implanting the tan-type BLF and introducing exquisite manipulation of sign functions,the technique of adding a power integrator is skillfully revamped to develop a state feedback control scheme.Finally,both theoretical analysis and simulation results verify that,the proposed scheme can ensure the system is finitetime stable in probability while preventing violation of a pre-specified output constraint.(2)For high-order stochastic nonlinear systems with output constraints and disturbances,a finite time controller is designed.Based on the given assumptions,a modified tan-type BLF is constructed to handle the output constraint issue of the considered system.Furthermore,the state feedback controller is designed step by step with the help of the adding a power integrator technique and the constructed BLF.Under the designed controller,the system states will converge to a small region of the origin in finite time and the output constraint can be achieved.(3)For high-order nonlinear stochastic systems with asymmetric output constraints,the problem of finite-time stabilization is addressed.The asymmetric constraint is more significance than the symmetric one from practical point of view,and it is more difficultly achieved since the asymmetric BLFs are not easily constructed and analyzed.To this end,a polynomial-type asymmetric BLF is constructed by fully utilizing the information of the upper bounding functions in nonlinear growth conditions.On this basis,a finite time control strategy is proposed by combining the asymmetric BLF with the improved adding a power integrator technique.The proposed strategy not only guarantees that the system is finite-time stable in probability but also ensures that the output constraint is not violated.(4)For high-order stochastic nonlinear systems with unknown nonlinearities,the problem of the adaptive fuzzy output-constrained control is considered.The assumptions of growth conditions for nonlinearities are removed,that is,no information of the nonlinear functions can be provided to the design procedure.In this case,a tan-type BLF,only depending on power exponents,is used to deal with the output constraint problem.Then,the fuzzy logic system is applied to approximate the unknown functions appearing in the design procedure,and the adaptive fuzzy control scheme is developed by the implanting the above BLF into adding a power integrator technique.Finally,through theoretical analysis and numerical simulation,it is shown that the designed controller can guarantee that all the variables of the closed-loop system are bounded in probability without violating the given output constraint.(5)For high-order stochastic nonlinear systems with nontriangular structure and unknown nonlinearities,the problem of the adaptive fuzzy control with asymmetric output constraints is solved.In practice,the nontriangular system with a more general form widely exists.For the nontriangular system,if using traditional backstepping method to design the controller,then every virtual controller would be the function of all the state variables,which causes the algebraic loops problem.To solve this obstacle,a skillful manipulation is employed to revamp the technique of adding a power integrator.First of all,a polynomial-type asymmetric BLF,which only depends on power exponents but is unconcerned with system nonlinearities,is constructed to cope with asymmetric output constraints.Then,the fuzzy logic system is used to approximate the unknown function in the design procedure,and the characteristics of the fuzzy basis function and the adding a power integrator technique are combined to design the adaptive fuzzy controller.Finally,through rigorous theoretical analysis demonstrates,it is proved that the designed controller can ensure that all the signals of the closed-loop system are bounded in probability with the achievement of the output constraint.