Homothetic tube model predictive control with multi-step predictors

We present a robust model predictive control (MPC) framework for linear systems facing bounded parametric uncertainty and bounded disturbances. Our approach deviates from standard MPC formulations by integrating multi-step predictors, which provide reduced error bounds. These bounds, derived from multi-step predictors, are utilized in a homothetic tube formulation to mitigate conservatism. Lastly, a multi-rate formulation is adopted to handle the incompatibilities of multi-step predictors. We provide a theoretical analysis, guaranteeing robust recursive feasibility, constraint satisfaction, and (practical) stability of the desired setpoint. We use a simulation example to compare it to existing literature and demonstrate advantages in terms of conservatism and computational complexity

Robust self-triggered model predictive control for discrete-time linear systems based on homothetic tubes

In this diploma thesis a robust self-triggered model predictive control (MPC) scheme for discrete-time linear time-invariant systems subject to input and state constraints and additive disturbances is presented. The goal of the proposed control scheme is to reduce the communication between the control computer and the sensors and actuators, respectively, while still providing robust stability. This is achieved by combining the ideas of self-triggered control, where the time between two samplings is maximized, and (Homothetic) Tube MPC, which is a robust optimization based control method. Tube MPC uses the so called tubes around the nominal state and input trajectories, based on the bounds of the disturbances, to ensure the satisfaction of the constraints. Homothetic Tube MPC is an enhancement with additional degrees of freedom. It is shown that a closed and bounded set including the origin in its interior is stabilized

A set-theoretic generalization of dissipativity with applications in Tube MPC

This paper introduces a framework for analyzing a general class of uncertain nonlinear discrete-time systems with given state-, control-, and disturbance constraints. In particular, we propose a set-theoretic generalization of the concept of dissipativity of systems that are affected by external disturbances. The corresponding theoretical developments build upon set based analysis methods and lay a general theoretical foundation for a rigorous stability analysis of economic tube model predictive controllers. Besides, we discuss practical prodecures for verifying set-dissipativity of constrained linear control systems with convex stage costs.Comment: 14 pages, 2 figure

Diseño de una unidad didáctica para la enseñanza de la homotecia mediante la metodología del análisis didáctico

Se presenta el planteamiento de una investigación que pretende fundamentar y elaborar una unidad didáctica para la enseñanza del concepto de homotecia en octavo grado de la Educación General Básica en Costa Rica (estudiantes de 14 años). Esto para atender las demandas curriculares de la reforma educativa establecida por el Ministerio de Educación Pública en el 2012 y proponer a los profesores de matemática una herramienta didáctica para la enseñanza de este concepto. Desde los principios del análisis didáctico, se plantean realizar los estudios conceptual, de contenido, cognitivo y de instrucción que fundamenten la selección y secuenciación de las tareas que se propongan, y, complementariamente, diseñar instrumentos de evaluación

A Linear Programming Approach to Computing Safe Sets for Software Rejuvenation

Software rejuvenation was born to fix operating system faults by periodically refreshing the run-time code and data. This mechanism has been extended to protect control systems from cyber-attacks. This letter proposes a software rejuvenation design method in discrete-time where invariant sets for the safety and mission controllers are designed to schedule the timing of software refreshes. To compute a minimal robust positively invariant (min-RPI) set and the bounded time between software refreshes to ensure system safety, an LP based approach is proposed for stable and unstable systems. Finally, the designed approach is illustrated by the case study of a simulated lab-scale microgrid

Learning-based control safeguarded by robust funnel MPC

Recently, a two component MPC scheme was introduced, consisting of pure feedback control (funnel control) and model-based predictive control (funnel MPC). It achieves output tracking of a given reference signal with prescribed performance of the tracking error for a class of unknown nonlinear systems. Relying on the feedback controller's ability to compensate for tracking errors even in the presence of noise and uncertainties, this control structure is robust with respect to model-plant mismatches and bounded disturbances. In the present article, we extend this control structure by a learning component in order to adapt the underlying model to the system data and hence to improve the contribution of MPC. Since the combined control scheme robust funnel MPC is inherently robust with respect to model-plant mismatches and the evolution of the tracking error in the prescribed performance funnel is always guaranteed, the additional learning component is able to perform the learning task online without an initial model or offline training