Mirko Fiacchini

Adaptive Control for a Mobile Robot Under Slip Conditions Using an LMI-Based Approach

This paper presents the synthesis of a control law which guarantees asymptotic stability for a wheeled mobile robot under slip conditions subject to both constraints and system dynamics. This control law is obtained using Linear Matrix Inequalities. The improvements provided by the pro- posed adaptive control are compared with other control laws, dealing with slip effect, through simulation.

Online robust tube-based MPC for time-varying systems: a practical approach

This article focuses on the design of a robust model predictive control law for constrained discrete-time time-varying systems with additive uncertainties. The proposed solution to the control problem is a tube-based MPC ensuring robustness and constraints fulfilment. Reachable sets are calculated online taking into account the system dynamics by means of an adaptive local control law and additive uncertainties. The proposed method represents a trade-off between small conservativeness and efficient real-time execution. This approach is applied to solve the trajectory tracking problem of a mobile robot. Simulation results provide a comparison between the tube-based MPC scheme and established motion control algorithms, showing the efficient execution and satisfactory behaviour of the proposed controller.

Brief paper: Convex invariant sets for discrete-time Lur'e systems

In this paper, a method to estimate the domain of attraction of a class of discrete-time Lure systems is presented. A new notion of invariance, denoted LNL-invariance, is introduced. An algorithm to determinate the largest LNL-invariant set for this class of systems is proposed. Moreover, it is proven that the LNL-invariant sets provided by this algorithm are polyhedral convex sets and constitute an estimation of the domain of attraction of the non-linear system. It is shown that any contractive set for the Lure system is contained in the LNL-invariant set obtained applying the results of this paper. Two illustrative examples are given.

Robust Tube-based Predictive Control for Mobile Robots in Off-Road Conditions

This paper focuses on the design of a tube-based Model Predictive Control law for the control of constrained mobile robots in off-road conditions with longitudinal slip while ensuring robustness and stability. A time-varying trajectory tracking error model is used, where uncertainties are assumed to be bounded and additive. The robust tube-based MPC is compared with other motion control techniques through simulation and physical experiments. These tests show the satisfactory behavior of the presented control strategy.

Approximate Reachability Analysis for Linear Discrete Time Systems Using Homothety and Invariance

Abstract This paper introduces a method for approximate reachability, for linear discrete time systems, based on homothety and set invariance. The proposed method utilizes two particular families of sets, more precisely their members, and particular forms of the approximation maps to obtain simple inner and outer approximate reachable sets/tubes. The resulting set–dynamics, induced by the uncertainty set, the underlying dynamics in the state space and the approximation maps, are restricted to these particular families of sets and under standard assumptions yield bounded and convergent approximate reachable sets/tubes. A tractable computational procedure is suggested and a few illustrative examples are provided.

Invariant Approximations of the Maximal Invariant Set or "Encircling the Square"

Abstract This paper offers a method for the computation of invariant approximations of the maximal invariant set for constrained linear discrete time systems subject to bounded, additive, disturbances. The main advantage of the method is that it generates invariant sets at any step of the underlying set iteration. Conditions under which the sequence of generated invariant sets is monotonically non–decreasing and converges to the maximal invariant set are provided. Explicit formulae for the estimates of the Hausdorff distance between the underlying iterates and the maximal invariant set are derived.

On the Computation of Robust Control Invariant Sets for Piecewise Affine Systems

In this paper, an alternative approach to the computation of control invariant sets for piecewise affine systems is presented. Based on two approximation operators, two algorithms that provide outer and inner approximations of the maximal robust control invariant set are presented. These algorithms can be used to obtain a robust control invariant set for the system. An illustrative example is presented.

Robust tube-based MPC for constrained mobile robots under slip conditions

This paper focuses on the design of a robust tube-based Model Predictive Control law for the control of constrained mobile robots. A time-varying trajectory tracking error model has been used, where uncertainties are assumed to be bounded and additive. The proposed solution to the control problem is a tube-based MPC ensuring robustness and stability. A comparative simulation example is presented showing the promising behavior of the robust MPC controller.

SYNTHESIS OF ROBUST SATURATED CONTROLLERS: AN SNS-APPROACH

Abstract In this paper, the notion of SNS-domain of attraction is applied to the synthesis of saturated controllers. The notion of SNS-domain was first introduced in the framework of estimation of the domain of attraction of a discrete saturated control system. The main contribution of this paper is an algorithm that allows to obtain a saturated control law for a linear system maximizing the domain of attraction. The parameters of the controller are obtained in such a way that the size of the corresponding polyhedric SNS-domain of attraction is maximized. It is well known that, for single input systems, the greatest ellipsoidal invariant set can be obtained by means of a control law that does not saturate in the corresponding ellipsoidal set. In this paper it is shown how saturated control laws yield to greater domain of attractions when polyhedric invariant sets are considered. That is, the algorithm proposed in this paper provides a controller with a domain of attraction that contains any pre-specified ellipsoidal control invariant set obtained by means of a non saturated control law.

A convex approximation of the feasible solution set for nonlinear bounded-error identification problems

A new nonlinear bounded-error identification method is presented in this paper. We consider models that depend non linearly on a given set of parameters. An additive bounded error term is included to take into account non modelled dynamics and disturbances in the measurements. The objective of the proposed methodology is to obtain the set of parameters that are consistent with a sequence of input- output measurements and the additive bounded error term. An iterative algorithm that provides a sequence of polyhedral outer bounds of this set is presented. At each iteration, a new improved outer bound is obtained adding some linear constraints to those defining the previous polyhedral outer bound. In this way, the volume of the outer approximation is shown to decrease at each iteration. The results of the paper rely on the representation of the functional form of the system by means of the difference of convex functions. An example is provided to illustrate the algorithm.