Improved Adaptive Dynamic Surface Control Of Output-constrained Systems

Considering the physical limitation of the devices,performance and safety specifications or other factors,almost all of the practical control systems are inevitably subject to constraints with various forms.During operation,violation of such constraints may result in system performance degradation or even lead to instability.On the other hand,with the rapid development of science and technology,the controlled objects are becoming increasingly complex,along with the increasing requirement for system control quality.Driven by both practical needs and theoretical challenges,control of output-constrained uncertain nonlinear systems has attracted tremendous attention in recent years.Dynamic surface control(DSC)is one of the mainstream nonlinear control design methods which was developed on the classical Backstepping method foundation.The DSC method shares the same advantages with Backstepping and eliminates the inherent ‘explosion of complexity' problem in the latter,and therefore,is favored in both theories and applications.However,for the designed DSC controllers,the closed-loop stability conditions are associated with system initial condition and reference trajectory,and the ranges of the design parameters are difficult to be a priori determined in theory.Besides,the steady state tracking accuracy cannot be specified a priori.These shortcomings make it difficult to choose appropriate parameters for controller implementation and bring inconvenience to the designer.The control design for output-constrained systems based on the existing DSC method will further increase the difficulty of parameters design and system debugging,and moreover,their values will also affect the size of the feasible initial output set.Motivated by the above considerations,this thesis proposes an improved adaptive DSC design method,and on this basis,systematically investigates the control design for uncertain lower-triangular nonlinear systems with output constraints.Besides,part of the developed theories is applied to longitudinal control of hypersonic vehicles with angle-of-attack(AOA)constraints.The main contents are outlined as follows:Firstly,an improved adaptive DSC method is proposed,which can overcome the deficiencies of the existing DSC method.The new approach introduces nonlinear adaptive filters to obviate the need for analytic computation of virtual signal derivatives in classical Backstepping method.Meanwhile,novel flat zone introduced Lyapunov func-tions are applied to analyze the closed-loop stability.The developed controller not only can guarantee all signals in the closed-loop system are uniformly ultimately bounded and the ultimate tracking error to achieve the accuracy given a priori,but also,the stability condition is independent of the system initial condition and reference trajectory,and the feasible ranges of the design parameters are provided in an explicit way.Thus,for control implementation,the design parameters can be freely chosen from the feasible ranges to improve the dynamic performance.Numerical simulation results further confirmed the effectiveness of the proposed approach.Secondly,for a class of uncertain strict-feedback nonlinear systems subject to timevarying asymmetric output constraints,two kinds of constrained control schemes,namely,the time-varying asymmetric barrier Lyapunov function(BLF)-based improved adaptive DSC scheme and the nonlinear mapping(NM)-based improved adaptive DSC scheme,are presented.With the application of the obtained controllers,all signals in the closedloop system are ultimately bounded and the system output can track the desired trajectory with the ultimate error satisfies the accuracy given a priori,while the output constraints are never violated.Compared with the existing results,both two schemes can enlarge the set of admissible initial outputs and thus relax the initial condition requirements.Besides,the ranges of the controller parameters can be completely determined a priori.Among them,the NM-based controller possesses a simpler structure and is easier to implement.Two simulation studies further demonstrate the effectiveness of the proposed methods.Thirdly,by using the NM-based improved adaptive DSC approach,the tracking control of output-constrained uncertain pure-feedback systems is investigated.To circumvent the difficulties arising from the nonaffine properties,two schemes are proposed.One is to use system transformation technique to convert the nonaffine system into an affine one,and then the constrained controller is designed by following the methodology for strict feedback system.The other is to make use of the nonaffine functions of the system and the controller is designed by fusing a novel change of coordinates.Following the idea of minimal learning parameters,by estimating the maximum of uncertain parameters instead of the parameters themselves in each design step,both the number of the online learning parameters and the over-parametrization problem are reduced.The designed controllers have much simpler structures with less computational burden and can avoid the circular design problem and the drawbacks of the approximation-based approaches,which arecommonly encountered in existing results.Simulation examples in the end further verify the validity and effectiveness of the theoretical results.Fourthly,the NM-based improved adaptive DSC approach is extended to solve output constraint problem for uncertain nonlinear systems with immeasurable states.By incorporating K-filters to estimate the unmeasured states,two control schemes are proposed for output-constrained parametric output feedback systems with known and unknown high-frequency gain sign,respectively.The rigorous stability analysis is performed.In the proposals,the whole design needs only ? steps with ? being the system relative degree,and the adaptive law is necessary only at the first design step.As a consequence,the complexity of the design procedure is dramatically reduced and the resulting controller is of much simpler structure.In particular,for solving the problem of unknown high-frequency-gain sign,the Nussbaum gain techniques are introduced and the proposed approach can prevent Nussbaum parameter drifts.The effectiveness of the developed output feedback control schemes are verified through some simulation examples.Fifthly,the design of longitudinal control system for hypersonic vehicle with the consideration of AOA constraint is investigated and a simple but very effective control strategy is proposed.The typical control-oriented hypersonic vehicle model is reasonably decomposed into velocity subsystem and altitude subsystem.The AOA constraint problem is regarded as output constraint problem of the attitude loop in altitude subsystem and the AOA feedback strategy is adopted to realize the direct control.Following this idea,the velocity command and the AOA command are designed by considering both mission and trajectory constraints,the design models for velocity loop and attitude loop are separately established and the corresponding adaptive control laws are also constructed.In the design of the attitude loop,the NM-based improved adaptive DSC approach is applied to ensure the AOA constraint satisfaction.With the application of the designed control laws,the actual velocity and AOA of the vehicle can track their respective reference trajectories and thus the desired flight task can be accomplished.Simulation results from the full nonlinear model show the developed controller can achieve satisfactory performance.