Study On Robust Control For Uncertain Systems With Actuator Saturation

The phenomenon of actuator saturation is frequently encountered in various systems, such as industrial engineering systems,biological systems and social economics models.The presence of actuator saturation in control systems usually degrades system performance or even cause instability.Therefore,the study of systems with actuator saturation has attracted a great deal of attention over the past decades by many researchers. On the other hand,the mathematical model for control system design is only an approximate description to the real plant owing to the complexity of controlled plant.So it is always impossible to obtain accurate mathematics model for the practical controlled plant.There exists some difference between the mathematical model and the real system. And the difference of which some measure is able to get usually can be described as the uncertainties in the model arguments.The objective of robust control theory is to design a control law such that the resultant closed-loop system is stable and satisfies some prescribed performance for all admissible uncertainties.The stability analysis and synthesis problem for systems with actuator saturation is investigated in this dissertation.For linear systems subject to actuator saturation,the domain of attraction of the closed-loop system is first studied.When uncertain parameters appear,the problems of robust stabilization,robust H_∞filtering,robust H_∞output feedback control for linear systems with saturated controls and parameters uncertainties are investigated respectively.The main contents of this dissertation are outlined as follows,(1) The problem of stability analysis of linear systems subject to actuator saturation is studied.Using affine saturation-dependent Lyapunov function approach,a new method is presented for estimating the domain of attraction.A family of linear matrix inequalities(LMIs) provides sufficient condition for the existence of the affine saturation-dependent Lyapunov function is presented.The results obtained can reduce the conservativeness compared to the existing ones.(2) The problem of local stabilization of continuous-time linear systems with control amplitude and rate saturation is proposed.The nonlinear effects introduced by the saturation in the closed-loop system are modeled by means of polytopic differential inclusion.Sufficient conditions,formulated in linear matrix inequalities (LMIs),are obtained to ensure local stabilization of the closed-loop systems.These conditions are then extended to design a controller with the aim of maximizing the domain of attraction of the closed-loop system,maximizing the upper bound on the norm of the disturbance or minimizing the L₂-gain from the disturbance to the controlled output.(3) The problem of robust H_∞filtering for a class of uncertain continuous-time systems with measurements saturation is investigated.Attention is focused on the analysis and synthesis problems of a full order robust H_∞filter such that the filtering error dynamics is asymptotically stable with a guaranteed disturbance rejection attenuation levelγ.It is shown that the filtering error dynamics obtained from the original system plus the filter can be modeled by a linear system with deadzone nonlinearity.Then based on a sector condition and the parameter-dependent Lyapunov function approach,sufficient conditions in an LMI form under which the desired filters exist are developed.These conditions are then considered in a convex optimization problem with LMIs constraints in order to design an optimal robust H_∞filter that maximizes an estimate of the domain of attraction for the filtering error system.(4) The problem of robust H_∞filter design for a class of uncertain discrete-time systems with saturated measurements is concerned.Attention is focused on the analysis and synthesis problems of a full order robust H_∞filter such that the filtering error dynamics is asymptotically stable with a guaranteed disturbance rejection attenuation levelγ.It is shown that the filtering error dynamics obtained from the original system plus the filter can be modeled by a linear system with deadzone nonlinearity.Then based on a sector condition,sufficient conditions in a linear matrix inequality(LMI) form under which the desired filters exist are developed. These conditions are then converted to a convex optimization problem with LMIs constraints in order to design an optimal robust H_∞filter that maximizes an estimate of the domain of attraction for the filtering error dynamics.(5) The problems of the stability analysis and design for uncertain stochastic systems with time-varying delays in state and actuator saturation is addressed.The parameter uncertainties belong to a convex polytopic set,and the delays are time varying.Sufficient conditions are obtained in terms of a priori designed feedback matrix for determining if a given set is in inside the domain of attraction.Using the LMI approach,an estimate of the domain of attraction is presented.The problem of designing a state feedback controller such that the domain of attraction is enlarged is formulated through solving an optimization problem with LMI constraints.(6) The problem of robust H_∞output feedback control for continuous-time systems with Markovian jump parameters and saturating controls is presented.It is shown that the closed-loop system obtained from the original system plus the controller can be modeled by a linear Markovian jump system with deadzone nonlinearity. Then a sector condition is used to tackle this nonlinearity.Robust H_∞output feedback control problem is to design a saturated controller ensuring the stochastic stability and a prescribed H_∞performance for the closed-loop systems.Sufficient conditions in an LMI form under which the desired controller exists are developed. The conditions are then considered in a convex optimization problem with LMIs constraints in order to design an optimal robust H_∞output feedback control law that maximizes an estimate of the domain of attraction for the closed-loop system. The conclusion and perspective are given at the end of the dissertation.