Nonlinear feedback laws for practical stabilization of systems with input and state constraints

Composite nonlinear control with state and measurement feedback for general multivariable systems with input saturation

In a quick motion system, the shortest setting time is usually pursued, while for a system existing both input constraint and state constraints, by using traditional reference governor, maybe there are one phenomenon: some state don't achieve maximal valve due to shape of invariant set, This will lead to a longer setting time. This paper provides a method to shorten setting time of output via an outer feedback based on traditional reference governor. Outer feedback is computed by solving a convex non-constrained quadratic optimization. For linear system with outer feedback, different invariant set is computed based on reference governor. Meanwhile, this paper describes a built process of serval invariant sets and provides a most big invariant set just to fulfill the first receding horizon to get the shortest setting time.

In this paper, the S-constrained controllability to a target set Sigma is studied for linear continuous-time systems with state and input constraints. A proximal aiming controller design scheme is presented, which involves a certain modification of the original dynamics. The modified dynamics in effect provide state constraint removal. Both a feasible near-set of initial states associated with the proposed feedback scheme and a procedure for obtaining the modified dynamics are also developed. The novel feature of the proposed discontinuous feedback control law is that it can steer the system state back to the interior of state constraint set S as quickly as possible when state arrives at (or near) the boundary of S. A numerical example is also given to illustrate the effectiveness of the design scheme.

The paper aims to discuss the issues of actuator saturation and external disturbance in the magnetic levitation (maglev) system. The proposed technique is composed of composite nonlinear feedback (CNF) and super-twisting algorithm (STA)-based integral sliding mode (ISM) control to tackle the problem of actuator saturation and external disturbances simultaneously. The composite nonlinear feedback scheme comprises of linear feedback law which provides stability and fast response whereas the nonlinear feedback law takes care of input saturation and reduces the overshoot. The super-twisting algorithm (STA)-based integral sliding mode (ISM) controller is designed for disturbance rejection. A super-twisting algorithm-based approach is applied on ISM scheme to eliminate the chattering effect and make it continuous in nature for its direct implementation to the physical maglev system. The designed scheme is successfully tested on real-time feedback instruments model of the maglev system.

On improvement of transient performance in tracking control for a class of nonlinear systems with input saturation

This paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions. A recently introduced non-quadratic Lyapunov function, the convex hull quadratic function, is used for the construction of nonlinear state feedback laws. Design objectives include stabilization with maximal convergence rate, disturbance rejection with minimal reachable set and least /spl Lscr//sub 2/ gain. Conditions for stabilization and performances are derived in terms of bilinear matrix inequalities (BMIs), which cover the existing linear matrix inequality (LMI) conditions as special cases. Optimization problems with BMI constraints are formulated and solved effectively by combining the path-following algorithm and the direct iterative algorithm. The design results are guaranteed to be at least as good as the existing results obtained from LMI conditions. In most examples, significant improvements on system performances have been achieved, which demonstrate the advantages of using nonlinear feedback control over linear feedback control for linear differential inclusions. It is also observed through numerical computation that nonlinear control strategies may help to reduce control effort substantially.

In this paper, the problem of optimal time-varying attitude tracking control for rigid spacecraft with system constraints and unknown additive disturbances is considered. Through the design of a new non-linear tube-based robust model predictive control (TRMPC) algorithm, a dual-loop cascaded tracking control framework is established. The proposed TRMPC algorithm explicitly considers the effect of disturbances and applies tightened system constraints to predict the motion of the nominal system. The obtained optimal control action is then combined with a non-linear feedback law such that the actual system trajectories can always be steered within a tube region centred around the nominal solution. To facilitate the recursive feasibility of the optimization process and guarantee the input-to-state stability of the tracking control process, the terminal controller and the corresponding terminal invariant set are also constructed. The effectiveness of using the proposed dual-loop TRMPC control scheme to track reference attitude trajectories is validated by experimental studies. A number of comparative studies were carried out, and the obtained results reveal that the proposed design is able to achieve more promising constraint handling and attitude tracking performance than that of the other newly developed methods investigated in this research.

This work develops a numerical algorithm for the calculation of an optimal nonlinear state feedback law for nonlinear systems. A quadratic performance index is used which contains quadratic error terms, and quadratic input penalty terms. The optimization problem is solved using the Hamilton-Jacobi equations, which determine the optimal nonlinear state feedback law. A Newton-Kantorovich iteration is developed for the solution of the pertinent Hamilton-Jacobi equations, which involves solving a Zubov partial differential equation, at each step of the iteration, using a power series method. At step N of the iteration, the method generates the (N + 1)-th order truncation of the Taylor series expansion of the optimal state feedback function. The method is applied to the problem of controlling a system of two non-isothermal continuous stirred tank reactors (CSTR), where an exothermic reaction takes place

Robust Output Feedback MPC for Linear Systems via Interpolation Technique

This paper investigates a novel robust adaptive dynamic surface control scheme based on the barrier Lyapunov function (BLF), online composite learning, disturbance observer, and improved saturation function. It is mainly designed for a class of skid-to-turn (STT) interceptor integrated guidance and control (IGC) design problems under multi-source uncertainties, state constraints, and input saturation. The serial-parallel estimation model used in this study estimates the system states and provides “critic” information for the neural network and disturbance observer; then, these three are combined to realize online composite learning of the multiple uncertainties of the system and improve the interception accuracy. In addition, the state and input constraints are resolved by adopting the BLF and the improved saturation function, while the design of the auxiliary system ensures stability. Finally, a series of simulation results show that the proposed IGC scheme with a direct-hit intercept strategy achieves a satisfactory effect, demonstrating the validity and robustness of the scheme.

Event-triggered adaptive control for multiple high-speed trains with deception attacks in bottleneck sections

We present an algorithm for steering the output of a linear system from a feasible initial condition to a desired target position, while satisfying input constraints and nonconvex output constraints. The system input is generated by a collection of local linear state-feedback controllers. The path-planning algorithm selects the appropriate local controller using a graph search, where the nodes of the graph are the local controllers and the edges of the graph indicate when it is possible to transition from one local controller to another without violating input or output constraints. We present two methods for computing the local controllers. The first uses a fixed-gain controller and scales its positive invariant set to satisfy the input and output constraints. We provide a linear program for determining the scale-factor and a condition for when the linear program has a closed-form solution. The second method designs the local controllers using a semi-definite program that maximizes the volume of the positive invariant set that satisfies state and input constraints. We demonstrate our path-planning algorithm on docking of a spacecraft. The semi-definite programming based control design has better performance but requires more computation.

We study the arbitrarily varying channel (AVC) with input and state constraints, when the encoder has state information in a causal or noncausal manner. For the causal state information setting, we develop lower and upper bounds on the random code capacity. A lower bound on the deterministic code capacity is established in the case of a message-averaged input constraint. In the setting where a state constraint is imposed on the jammer, while the user is under no constraints, the random code bounds coincide, and the random code capacity is determined. Furthermore, for this scenario, a generalized non-symmetrizability condition is stated, under which the deterministic code capacity coincides with the random code capacity. For the noncausal state information setting, we determine the random code capacity of the AVC under input and state constraints. In addition, a condition on the channel is stated, under which the deterministic code capacity coincides with the random code capacity.

Input and state constraints have always been a practical consideration in engineering systems. How to address such constraints, especially when the actuator is subject to unknown faults, is of practically important. In this work, we present a novel adaptive fault tolerant control (FTC) scheme for a class of multi-input multi-output (MIMO) nonlinear systems with input and state constraints and subject to multiplicative and additive actuator faults. We show that under the proposed adaptive FTC scheme, exponential convergence of the output tracking error into a small neighbourhood of zero is guaranteed, while the constraints on the system state will not be violated during operation. All closed loop signals are shown to be bounded. An illustrative example is presented to demonstrate the effectiveness of the proposed FTC scheme.

In this paper, the constrained control of systems evolving on matrix Lie groups with uncertainties is considered. The proposed methodology is composed of a nominal Model Predictive Control (MPC), and a feedback controller. The previous work on the control of systems on manifolds is applied to design the nominal MPC, which generates the nominal trajectory. In the nominal MPC, the state and input constraints on the Lie group are transformed into the constraints on the Euclidean space. While to deal with uncertainties, the feedback control used to track the nominal trajectory is designed directly on the Lie group. The tracking error in the feedback control is proved to be bounded in invariant sets, which are further used to revise the constraints in nominal MPC. We prove that the input‐to‐state stability of the entire system under the proposed control methodology with respect to the disturbances can be achieved. The proposed methodology is applied to the constrained attitude control of rigid bodies with uncertainties. In the application example, the detailed mathematical proof and the comparative numerical simulation are presented to demonstrate the feasibility of the proposed methodology.