Control Of Nonlinear Systems Under State And Performance Constraints

Most practical engineering systems are characterized with complex structures,high nonlinearities and strong dynamic couplings,yet operating under severe and dynamic environment,making the control problem of such systems rather complicated.Furthermore,due to the security and prescribed performance considerations and certain physical limitations,the corresponding systems are expected to operate stably and reliably under constraints,posing significant challenges to controller design and stability analysis,which has attracted increasing research attention from the control community.In this thesis,the state-constrained control and the prescribed performance control of nonlinear systems are studied,respectively.The main contents and contributions are shown as follows:(1)The problem of output-constrained control of strict-feedback nonlinear systems with parametric uncertainties is investigated.Firstly,by constructing an output-dependent nonlinear transfer function,the problem of asymmetric output constraint is converted into the boundedness problem of such function.Secondly,upon utilizing the standard backstepping technique,an adaptive tracking control algorithm for nonlinear systems under output constraint and parametric uncertainties is proposed,which not only ensures that the piecewise Log-Asymmetric Barrier Lyapunov Function is not required,greatly reducing the complexity of system stability analysis,but also relaxes the initial condition of system output.In addition,by improving the nonlinear transfer function,such algorithm can also handle the case of time-varying output constraint.(2)For the strict-feedback nonlinear systems with nonparametric uncertainties,the full-state constrained control is developed.Different from the normally used Barrier Lyapunov Function(BLF)and Integral BLF,a full-state-dependent nonlinear transfer function is established and it is proved that the stabilization of such function is sufficient to solve the problem of full-state constraints.Then we introduce a new coordinate transformation and integrate it into each step of dynamic surface control based backstepping design,perfectly solving the problem of state constraints and completely circumventing the demanding “feasibility conditions” on virtual controllers.Consequently,there is no need for the tedious offline computations for feasibility verification,allowing the designer more freedom to select design parameters and rendering the solution more user-friendly in design and implementation.In addition,the utilization of dynamic surface control effectively solves the problem of “differential explosion” in the traditional backstepping method.(3)Computational burden is an important indicator for evaluating the strengths and weaknesses of the corresponding controller.Therefore,for the multi-input multi-output nonlinear systems with unknown time-varying gain matrix and nonparametric uncertainties,a single-parameter-estimation based full-state constrained control is studied.Upon employing the state-dependent nonlinear transfer function,the developed control method can handle the symmetric/asymmetric constraints directly without the need for converting the state constraints into new constraints on tracking errors(as used in the BLF in most existing works),relaxing the restrictions on initial states;By applying the upper bound estimation technique and core-information method,only one single parameter updating is needed,significantly reducing the design complexity and online computation burden.Furthermore,the developed nonlinear transfer function can cope with both constrained and unconstrained cases simultaneously such that redesigning controllers and reanalyzing stability of nonlinear systems are not required.(4)Although the aforementioned control solutions are available for strict-feedback nonlinear systems under output/state constraints and the feasibility conditions are removed,the corresponding control algorithms have additional requirements on the constraint boundaries and cannot deal with the dynamic state constraints.Here we develop a control solution for strict-feedback nonlinear systems capable of coping with a wide class of asymmetric constraints imposed dynamically,yet without involving the notorious feasibility conditions.Firstly,in order to deal with the problem of dynamic constraints and eliminate the limitations on the constraint boundaries,a unified nonlinear transfer function is constructed and the state-constrained control algorithm is further developed.The rigorous stability analysis and proof are given by using the Lyapunov stability theory and the dynamic surface control method,through which all signals in the closed-loop systems are semi-globally bounded and the demanding feasibility conditions on virtual controllers are avoided.(5)Adaptive control with exponential stabilization is a desired performance in control community.However,most of the existing works can only achieve stabilization asymptotically.Here we develop an adaptive control scheme for linear or nonlinear systems to achieve exponential stabilization via transformational approach.Firstly,for the stabilization of first-order linear systems with unknown parameters,by employing a constant transformation the exponential convergence of system state can be ensured.However,the convergence rate relies on the initial values of systems,which indicates that the convergence rate is not uniform with the initial conditions.Secondly,by constructing an exponential transformation,we develop an adaptive control for first-order linear systems such that the system state converges to zero with a predetermined decay rate,which is independent of initial conditions and is at user's disposal.Then we turn our attention from the “matched” scalar linear example to the general class of strict-feedback nonlinear systems.A new backstepping coordinate transformation is constructed by employing exponential transformation,with which an adaptive stabilization control algorithm is designed to ensure that the states of system converge to zero and the decay rate of exponential stabilization is independent of initial conditions and can be pre-specified.Furthermore,by using the Lyapunov stability analysis,all signals in the closed-loop systems are globally bounded.(6)Stabilization is a special case of tracking problem,to apply the above transformation approach for tracking control of nonlinear systems and to achieve satisfactory tracking performance,a robust adaptive “accelerated” control scheme for MIMO nonlinear systems with nonparametric uncertainties and unknown control gain matrices is developed.By introducing the concept of rate function and constructing an increasing yet bounded function,a time-varying transformation in terms of tracking error is proposed such that the tracking performance in transient and steady-state can be adjusted by properly selecting rate functions and design parameters.The global stability of closed-loop system is proved by Lyapunov stability theory and the proposed algorithm avoids excessively large initial driving efforts,reducing damages on actuators.