Alessandro Casavola

A predictive reference governor for constrained control systems

A method based on conceptual tools of predictive control is described for solving tracking problems wherein pointwise-in-time input and/or state inequality constraints are present. It consists of adding to a primal compensated system a nonlinear device called reference governor (RG) whose action is based on the current state, set-point, and prescribed constraints. The aim of the RG device is that of modifying, when necessary, the reference in such a way that the constraints are enforced and the primal compensated system maintains its linear behavior. The RG action is computed on-line by solving, at each sampling time, a constrained quadratic programming problem that usually requires low computational times also for systems of relatively high order. The overall system is proved to fulfill the constraints, be asymptotically stable, and exhibit an offset-free tracking behaviour, provided that an admissibility condition on the initial state is satisfied.

Reference governor for constrained uncertain linear systems subject to bounded input disturbances

A method is presented for designing robust reference governors for uncertain discrete-time linear systems in the presence of unknown but bounded input disturbances and pointwise-in-time input and/or state constraints. A reference governor is a nonlinear device which is added to a primal compensated linear system in order to modify, when necessary, the reference signal in such a way the constraints are enforced and the compensated system maintains its linear behaviour. The present solution extends previous results in various directions.

Continuous-time LQ regulator design by polynomial equations

Abstract The deterministic continuous-time LQ output regulation problem is solved by polynomial equations as an alternative to the usual Riccati equation approach. In particular, it is shown that Riccati-based and polynomial methods are fully conceptually equivalent in steady-state LQ regulation.

Ellipsoidal low-demanding MPC schemes for uncertain polytopic discrete-time systems

A model predictive control (MPC) method based on ellipsoidal calculus is described in order to address the control problems in the presence of state and input constraints for uncertain polytopic linear plants under persistent disturbances. In order to reduce the usually high numerical complexity and conservatism associated to polytopic robust MPC schemes the present approach consists of moving off-line most part of the computational burden and using closed-loop predictions. An example is also presented.

A nonlinear command governor for constrained control systems

Abstract A method based on conceptual tools of predictive control is described for solving tracking problems wherein pointwise-in-time input and/or state inequality constraints are present. It consists of adding to a primal compensated system a nonlinear device called command governor (CG) whose action is based on the current state, set-point and prescribed constraints. The overall system is proved to fulfill the constraints, be asymptotically stable, and exhibit an offset-free tracking behaviour, provided that an admissibility condition on the initial state is satisfied.

Minimization of a closed-loop response to a fixed input for SISO systems

It is shown that the problem of minimizing a regulated response of a single-input/single-output system due to a fixed bounded input can be converted, via polynomial techniques, to a linear infinite-dimensional Chebyshev data fitting problem. Approximating feasible solutions within any specified degree of accuracy can be obtained by converting the original problem into a sequence of increasingly large, finite-dimensional Chebyshev approximation problems, for which solution stable and efficient numerical methods exist. A direct formula for calculating tight upper-bounds to the approximation error is provided. The link between the present algebraic approach and the Dahleh and Pearson functional analytic one (1988) is also discussed.

H∞ and H2 simple controllers for robotic applications

A new method is discussed which allows one to synthesize continuous-time controllers of lead/lag or PID type that are optimal both in the H∞ and H2 sense (equalizing H2 controllers), for a restricted class of systems well suited for robotic applications. In particular, conditions on the plant are given so that the optimal controller has a lead/lag or PID structure in cascade with an additional low-pass filter. The method is applied to synthesize a PI controller for the velocity control of one joint of an electrically actuated industrial SCARA robot.

Formation flying control of a pair of nano-satellites based on switching predictive control

This paper provides an implementable and energy efficient solution for the problem of manoeuver control of formations of nano-satellites subject to input-saturation constraints and persistent disturbances. The proposed control scheme is based on a supervisory switching logic which, at any time instant, select the most appropriate controller from a bank of pre-computed candidate predictive regulators. Each candidate controller is tuned for minimal energy control on to a different control horizon. The larger the control horizon, the smaller the energy of the required inputs. An example is provided for showing the effectiveness of the proposed approach.

Robust predictive control of input-saturated uncertain systems

A robust predictive controller for input-saturated LTV discrete-time systems with polytopic model uncertainties is presented. The solution is based on the minimization, at each time instant, of an upper-bound of the worst-case infinite horizon quadratic cost under the constraint of steering the set-valued future state evolutions emanating from the current state into a feasible and positive invariant set. A condition on the initial state is given that suffices to ensure problem solvability for all subsequent time instants. Under the latter, the proposed predictive controller is proved to robustly asymptotically stabilize the input-saturated LTV polytopic system.

Predictive Controllers for Input Saturated Industrial Plants

Abstract The paper addresses the problem of stabilizing linear plants subjert to input saturation. A new Model Predictive Control (MPC) scheme is presented and contrasted with other known MPC schemes. It is shown that the new scheme ensures global exponential stability for plants with all their eigenvalues on the closed unit disk and, as a further benefit, performance can also be taken into account. An example is enclosed in order to support the results.