Nonlinear Receding-Horizon Control of Rigid Link Robot Manipulators

The approximate nonlinear receding-horizon control law is used to treat the trajectory tracking control problem of rigid link robot manipulators. The derived nonlinear predictive law uses a quadratic performance index of the predicted tracking error and the predicted control effort. A key feature of this control law is that, for their implementation, there is no need to perform an online optimization, and asymptotic tracking of smooth reference trajectories is guaranteed. It is shown that this controller achieves the positions tracking objectives via link position measurements. The stability convergence of the output tracking error to the origin is proved. To enhance the robustness of the closed loop system with respect to payload uncertainties and viscous friction, an integral action is introduced in the loop. A nonlinear observer is used to estimate velocity. Simulation results for a two-link rigid robot are performed to validate the performance of the proposed controller. Keywords: receding-horizon control, nonlinear observer, robot manipulators, integral action, robustness

Disturbance Observer-based Robust Control and Its Applications: 35th Anniversary Overview

Disturbance Observer has been one of the most widely used robust control tools since it was proposed in 1983. This paper introduces the origins of Disturbance Observer and presents a survey of the major results on Disturbance Observer-based robust control in the last thirty-five years. Furthermore, it explains the analysis and synthesis techniques of Disturbance Observer-based robust control for linear and nonlinear systems by using a unified framework. In the last section, this paper presents concluding remarks on Disturbance Observer-based robust control and its engineering applications.Comment: 12 pages, 4 figure

Sparse and Constrained Stochastic Predictive Control for Networked Systems

This article presents a novel class of control policies for networked control of Lyapunov-stable linear systems with bounded inputs. The control channel is assumed to have i.i.d. Bernoulli packet dropouts and the system is assumed to be affected by additive stochastic noise. Our proposed class of policies is affine in the past dropouts and saturated values of the past disturbances. We further consider a regularization term in a quadratic performance index to promote sparsity in control. We demonstrate how to augment the underlying optimization problem with a constant negative drift constraint to ensure mean-square boundedness of the closed-loop states, yielding a convex quadratic program to be solved periodically online. The states of the closed-loop plant under the receding horizon implementation of the proposed class of policies are mean square bounded for any positive bound on the control and any non-zero probability of successful transmission

Stochastic disturbance rejection in model predictive control by randomized algorithms

In this paper we consider model predictive control with stochastic disturbances and input constraints. We present an algorithm which can solve this problem approximately but with arbitrary high accuracy. The optimization at each time step is a closed loop optimization and therefore takes into account the effect of disturbances over the horizon in the optimization. Via an example it is shown that this gives a clear improvement of performance although at the expense of a large computational effort

Stochastic Model Predictive Control with Discounted Probabilistic Constraints

This paper considers linear discrete-time systems with additive disturbances, and designs a Model Predictive Control (MPC) law to minimise a quadratic cost function subject to a chance constraint. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalising violation probabilities close to the initial time and ignoring violation probabilities in the far future, this form of constraint enables the feasibility of the online optimisation to be guaranteed without an assumption of boundedness of the disturbance. A computationally convenient MPC optimisation problem is formulated using Chebyshev's inequality and we introduce an online constraint-tightening technique to ensure recursive feasibility based on knowledge of a suboptimal solution. The closed loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition.Comment: 6 pages, Conference Proceeding

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Model Predictive Control: Multivariable Control Technique of Choice in the 1990s?

The state space and input/output formulations of model predictive control are compared and preference is given to the former because of the industrial interest in multivariable constrained problems. Recently, by abandoning the assumption of a finite output horizon several researchers have derived powerful stability results for linear and nonlinear systems with and without constraints, for the nominal case and in the presence of model uncertainty. Some of these results are reviewed. Optimistic speculations about the future of MPC conclude the paper