There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Survey paper: Set invariance in control

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

Predictive Control for Linear and Hybrid Systems

An apposite and eminently readable reference for all behavioral science research and development

Encyclopedia of Statistics in Behavioral Science

The problem of confining the trajectory of a linear discrete-time system in a given polyhedral domain is addressed through the concept of (A, B)-invariance. First, an explicit characterization of (A, B)-invariance of convex polyhedra is proposed. Such characterization amounts to necessary and sufficient conditions in the form of linear matrix relations and presents two major advantages compared to the ones found in the literature: it applies to any convex polyhedron and does not require the computation of vertices. Such advantages are felt particularly in the computation of the supremal (A, B)-invariant set included in a given polyhedron, for which a numerical method is proposed. The problem of computing a control law which forces the system trajectories to evolve inside an (A, B)-invariant polyhedron is treated as well. Finally, the (A, B)-invariance relations are generalized to persistently disturbed systems.

(A,B)-invariant polyhedral sets of linear discrete-time systems

This paper presents and discusses the implementation results of a model-predictive control (MPC) scheme with friction compensation applied to trajectory following of an omnidirectional three-wheeled robot. A cascade structure is used with an inverse kinematics block to generate the velocity references given to the predictive controller. Part of the control effort is used to compensate for the effects of static friction, allowing the use of efficient algorithms for linear MPC with constraints. Experimental results show that the proposed strategy is efficient in compensating for frictional effects as well as for tracking predefined trajectories.

Design and Implementation of Model-Predictive Control With Friction Compensation on an Omnidirectional Mobile Robot

Model predictive control (MPC) theory has gained attention with the recent increase in the processing power of computers that are now able to perform the needed calculations for this technique. This kind of control algorithms can achieve better results in trajectory tracking control of mobile robots than classical control approaches. In this paper, we present a review of recent developments in trajectory tracking control of mobile robot systems using model predictive control theory, especially when nonholonomicity is present. Furthermore, we point out the growth of the related research starting with the boom of mobile robotics in the 90s and discuss reported field applications of the described control problem. The objective of this paper is to provide a unified and accessible presentation, placing the classical model, problem formulations and approaches into a proper context and to become a starting point for researchers who are initiating their endeavors in linear/nonlinear MPC applied to nonholonomic mobile robots. Finally, this work aims to present a comprehensive review of the recent breakthroughs in the field, providing links to the most interesting and successful works, including our contributions to state-of-the-art.

Nonholonomic mobile robots' trajectory tracking model predictive control: a survey

Trajectory tracking for autonomous vehicles is usually solved by designing control laws that make the vehicles track predetermined feasible trajectories based on the trajectory error. This type of ...

https://journals.sagepub.com/doi/pdf/10.1177/1729881418760461

Carlos E. T. Dorea

Papers

(A,B)-invariant polyhedral sets of linear discrete-time systems

Design and Implementation of Model-Predictive Control With Friction Compensation on an Omnidirectional Mobile Robot

Nonholonomic mobile robots' trajectory tracking model predictive control: a survey

Nonlinear model predictive control for trajectory tracking of nonholonomic mobile robots: A modified approach

(A, B)-invariance conditions of polyhedral domains for continuous-time systems