A Robust Constrained Reference Governor Approach using Linear Matrix Inequalities

The purpose of this paper is to examine and provide a solution to the output reference tracking problem for uncertain systems subject to input saturation. As well-known, input saturation and modelling errors are very common problems at industry, where control schemes are implemented without accounting for such problems. In many cases, it is sometimes difficult to modify the existing implemented control schemes being necessary to provide them with external supervisory control approaches in order to tackle problems with constraints and modelling errors. In this way, a cascade structure is proposed, combining an inner loop containing any proper controller with an outer loop where a generalized predictive controller (GPC) provides adequate references for the inner loop considering input saturations and uncertainties. Therefore, the contribution of this paper consists in providing a state space representation for the inner loop and using linear matrix inequalities (LMI) to obtain a predictive state-vector feedback in such a way that the input reference for the inner loop is calculated to satisfy robust tracking specifications considering input saturations. Hence, the final proposed solution consists in solving a regulation problem to a fixed reference value subjected to a set of constraints described by several LMI and bilinear matrix inequalities (BMI). The main contribution of the paper is that the proposed solution is a non-linear setpoint tracking approach, that is, it is allowed that the system goes into saturation facing the problem of setpoint tracking instead of regulating to the origin. An illustrative numerical example is presented.Ministerio de Ciencia y Tecnología DPI2004-07444-C04-01/0

Decoupled Reference Governors for Multi-Input Multi-Output Systems

In this work, a computationally efficient solution for constraint management of square multi-input multi-output (MIMO) systems is presented. The solution, referred to as the Decoupled Reference Governor (DRG), maintains the highly-attractive computational features of scalar reference governors (SRG) compared to Vector Reference Governor (VRG) and Command Governor (CG). This work focuses on square MIMO systems that already achieve the desired tracking performance. The goal of DRG is to enforce output constraints and simultaneously ensure that the degradation to tracking performance is minimal. DRG is based on decoupling the input-output dynamics of the system so that every channel of the system can be viewed as an independent input-output relationship, followed by the deployment of a bank of scalar reference governors for each decoupled channel. We present a detailed set-theoretic analysis of DRG, which highlights its main characteristics. A quantitative comparison between DRG, SRG, and the VRG is also presented in order to illustrate the computational advantages of DRG. Finally, a distillation process is introduced as an example to illustrate the applicability of DRG

A Passivity-Based Distributed Reference Governor for Constrained Robotic Networks

This paper focuses on a passivity-based distributed reference governor (RG) applied to a pre-stabilized mobile robotic network. The novelty of this paper lies in the method used to solve the RG problem, where a passivity-based distributed optimization scheme is proposed. In particular, the gradient descent method minimizes the global objective function while the dual ascent method maximizes the Hamiltonian. To make the agents converge to the agreed optimal solution, a proportional-integral consensus estimator is used. This paper proves the convergence of the state estimates of the RG to the optimal solution through passivity arguments, considering the physical system static. Then, the effectiveness of the scheme considering the dynamics of the physical system is demonstrated through simulations and experiments.Comment: 8 pages, International Federation of Automatic Conference 2017, 8 figure

Control synthesis for an unmanned helicopter with time-delay under uncertain external disturbances

This paper presents the controller synthesis for an unmanned helicopter with minimum initial information about the parameters of its mathematical model with time-delays of measured and control signals. The unknown parameters, wind disturbances, and system nonlinearity are considered as external disturbances that are estimated using a multi-gap observer. The estimates obtained are used in the control law to improve the stability rate for flight regimes

Dynamical Systems, Stability, and Chaos

In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics and control theory, and focussing on qualitative theory. From this perspective we show how concepts of stability enable us to classify dynamical equations and their solutions and connect the key issues of nonlinearity, bifurcation, control, and uncertainty that are common to time-dependent problems in natural and engineered systems. We discuss stability and bifurcations in three simple model problems, and conclude with a survey of recent extensions of stability theory to complex networks.Comment: 28 pages, 10 figures. 26/04/2007: The book title was changed at the last minute. No other changes have been made. Chapter 1 in: J.P. Denier and J.S. Frederiksen (editors), Frontiers in Turbulence and Coherent Structures. World Scientific Singapore 2007 (in press