Dynamic Output Feedback Robust MPC with Input Saturation Based on Zonotopic Set-Membership Estimation

Off-line approach to dynamic output feedback robust model predictive control

This paper is concerned with analyzing a novel model transformation of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new auxiliary model is proposed by employing a new approximation for time-varying delay state, and then delay partitioning method is used to analyze the scaled small gain of this auxiliary model. A sufficient condition on discrete-time T-S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced l 2 disturbance attenuation performance, is derived by employing the scaled small gain theorem. Then the solvability condition for the induced l 2 DOF control is also established, by which the DOF controller can be found by solving a set of linear matrix inequalities (LMIs).

ABSTRACTThe output feedback robust model predictive control (MPC), for the linear parameter varying (LPV) system with norm-bounded disturbance, is addressed, where the model parametric matrices are only known to be bounded within a polytope. The previous techniques of norm-bounding technique, quadratic boundedness (QB), dynamic output feedback, and ellipsoid (true-state bound; TSB) refreshment formula for guaranteeing recursive feasibility, are fused into the newly proposed approaches. In the notion of QB, the full Lyapunov matrix is applied for the first time in this context. The single-step dynamic output feedback robust MPC, where the infinite-horizon control moves are parameterised as a dynamic output feedback law, is the main topic of this paper, while the multi-step method is also suggested. In order to strictly guarantee the physical constraints, the outer bound of the true state replaces the true state itself, so tightness of this bound has a major effect on the control performance. In order to tighten the TSB, a procedure for refreshing the real-time ellipsoid based on that of the last sampling instant is given. This paper is conclusive for the past results and far-reaching for the future researches. Two benchmark examples are given to show the effectiveness of the novel results.

This paper considers the design problem of dynamic output feedback control for fractional-order (FO) Takagi-Sugeno fuzzy systems with uncertain parameters. Via the application of FO system stability theory, robust control method and the linear matrix inequality techniques, sufficient conditions are given for the stability analysis and the existence of the dynamic fuzzy output feedback controllers. The dynamic output feedback controller designed here guarantees the robust stability of the closed-loop system. Finally, a fractional order chaotic system simulation example is given to illustrate the effectiveness of the design approach here.

In this paper, the problem of L 2 -L ∞ dynamic output feedback controller design for the nonlinear switched system in the T-S fuzzy framework is investigated. First, the average dwell time approach is used to stabilize the nonlinear switched systems under an arbitrary switching law. Then, based on the piecewise Lyapunov function, the fuzzy-rule-dependent dynamic output feedback controller is designed to ensure that the overall closed-loop system is exponentially stable with a weighted :L 2 -L ∞ performance. Finally, the solvability condition of the desired output feedback controller is obtained by the linearization procedure technique, which can be calculated by available software.

Dynamic output feedback controller design for affine T–S fuzzy systems with quantized measurements

The problem of robust stabilisation is considered for uncertain systems using linear static output feedback (SOF) controllers and linear dynamical output feedback (DOF) controllers with fixed order. The existence conditions of output feedback controllers are given by matrix inequalities and result in some nonlinear optimisation problems. A class of uncertain plants whose nominal systems are minimal phase with a full row rank can be robustly stabilised by an SOF controller and DOF controller with any order, and controllers can be obtained by solving some linear matrix inequalities (LMIs). The method is demonstrated by two numerical examples

In this paper, the $\boldsymbol{L}_{\infty}$ control synthesis problem for linear systems subject to actuator saturation and persistent bounded disturbance is studied. An $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator are simultaneously designed. First, by using the quadratic Lyapunov function technique, a sufficient condition on the existence of the $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator is established via linear matrix inequalities (LMIs). Such an integrated controller is able to guarantee the regional stabilization and the $\boldsymbol{L}_{\infty}$ performance of linear systems with actuator saturation and external persistent bounded disturbance. Second, novel algorithms are developed to optimize the upper bound on the $\boldsymbol{L}_{\infty}$ performance, the event-triggered threshold and the domain of attraction. Moreover, an output-based event-triggered mechanism applying to the anti-windup dynamic output feedback control design is provided, which reduces the number of control actuation updates and information transmission with respect to the traditional time-triggered control scheme.

This paper is devoted to the problems of non-fragile H∞ and L2–L∞ control for a class of linear systems with time-varying state delay. The purpose is to design a dynamic output feedback controller with additive gain variations such that the closed-loop system is asymptotically stable while satisfying a prescribed H∞ (or L2–L∞) performance level. By using linear matrix inequality approach, a delay-dependent stability criterion is obtained by introducing a new type of Lyapunov–Krasovskii functional. Based on the obtained criterion, sufficient conditions for the existence of desired controllers are derived, and the corresponding stabilisation dynamic output feedback controller design algorithm is proposed. Numerical examples are included to illustrate the benefit and effectiveness of the proposed method.

Gain-scheduled Composite Non linear Feedback (CNF) control has been implemented to Continuous Stirred Tank Reactor (CSTR) in this work. Chemical reaction takes place inside the CSTR, which is adjured from high residual concentration to low residual concentration. Control of CSTR is a bit complex, as it requires complete dynamic study and its implementation. During the entire process, the reaction kinetics changes from stable-unstable-stable range with the decrease in residual concentration. To stabilize the reaction, appropriate cooling is necessary, to ensure that overheating of the CSTR doesn't occur. Gain-scheduled composite non linear feedback controller has been implemented successfully for better tracking performance and error has been computed in terms of Integral of Absolute Error (IAE). The novelty of the work lies in lesser error obtained for this particular model of CSTR. Comparison of the IAE has been done with Model Reference Adaptive Control (MRAC) MIT control in CSTR.

This paper suggests sufficient conditions for asymptotically stable dynamical output feedback controller design based on the circle criterion. It is shown that a dynamic output feedback stabilization problem with impending problems of finite escape time, previously attacked by observer-based design, can be successfully solved using circle criterion design. Stability of the closed-loop system is global and robust to parameter uncertainty.

Absolute stabilization of Lur’e systems via dynamic output feedback

In this paper, the event-triggered dynamic output feedback controller design problem is addressed for a class of discrete-time nonlinear systems in network environment. An augmented closed-loop system is constructed and the sufficient conditions to ensure the mean-square asymptotically stability of the closed-loop system with a Hankel-norm performance by considering the event-triggered condition and using the reciprocally convex technique. It is shown that the solution of the fuzzyrule-dependent dynamic output feedback controller parameters can be obtained by variable substitution method. An example is provided to demonstrate the effectiveness of the proposed design method.

We present the design of a Gain-Scheduled Mean-Field-Type Control (GS-MFTC) for a non-linear Continuous Stirred Tank Reactor (CSTR). The MFTC controllers belong to a class of stochastic control techniques considering the distribution of the system states, and control inputs, while minimizing the variance of both variables of interest. The underlying risk-aware control problem is solved explicitly for the infinite horizon in order to determine the required gains composing the feedback control input law. We present both the risk-neutral approach involving the first and second moment (mean and variance terms), and the risk-sensitive approach involving higher-order terms.

In terminal guidance phase, only partial information concerning the interception geometry is available. To intercept a target in specified direction under this condition, an impact angle constrained guidance law is proposed based on the dynamic output feedback. The guidance law doesn't use the rate of line-of-sight angle, and can guarantee convergence speed of the closed-loop system. Utilizing the parametric algebraic Riccati equation, a dynamic output feedback controller is designed. The controller contains a feedback law and an observer is obtained. Through integrated design of the parameters of the feedback law and the observer, the closed-loop system can be transformed to a new system, whose system matrix is a Jordan matrix. Using Lyapunov approach, desired convergence speed of the new system can be obtained by tuning its poles. And the same convergence speed of the original closed-loop system can also be achieved. Based on the dynamic output feedback controller, an impact angle constrained guidance law is derived. The guidance law is demonstrated by numerical simulation. Convergence speed can be guaranteed by the guidance law, and high guidance precision is achieved.