Miad Moarref

Stability and stabilization of linear sampled-data systems with multi-rate samplers and time driven zero order holds

In multi-rate sampled-data systems, a continuous-time plant is controlled by a discrete-time controller which is located in the feedback loop between sensors with different sampling rates and actuators with different refresh rates. The main contribution of this paper is to propose sufficient Krasovskii-based stability and stabilization criteria for linear sampled-data systems, with multi-rate samplers and time driven zero order holds. For stability analysis, it is assumed that an exponentially stabilizing controller is already designed in continuous-time and is implemented as a discrete-time controller. For each sensor (or actuator), the problem of finding an upper bound on the lowest sampling frequency (or refresh rate) that guarantees exponential stability is cast as an optimization problem in terms of linear matrix inequalities (LMIs). Furthermore, sufficient conditions for controller synthesis are formulated as LMIs. It is shown through examples that choosing the right sensors (or actuators) with adequate sampling frequencies (or refresh rates) has a considerable impact on stability of the closed-loop system.

Asymptotic stability of piecewise affine systems with sampled-data piecewise linear controllers

This paper addresses stability analysis of closed-loop sampled-data piecewise affine (PWA) systems. In particular, we study the case in which a PWA plant is in feedback with a sampled-data piecewise linear (PWL) controller. We consider the sampled-data system as a continuous-time system with a variable time delay. The contributions of this work are threefold. First, we present a modified Lyapunov-Krasovskii functional (LKF) for studying PWA systems with time delay. Second, based on the new LKF, sufficient conditions are provided for asymptotic stability of PWA systems in feedback with sampled-data PWL controllers. Finally, following the time-delay approach, we formulate the problem of finding a lower bound on the maximum delay that preserves asymptotic stability to the origin as an optimization program in terms of LMIs. The new results are successfully applied to a unicycle example.

Exponential stability and stabilization of linear multi-rate sampled-data systems

This paper addresses stability analysis and controller synthesis for linear multi-rate sampled-data systems. In these systems, a plant with linear dynamics is controlled by a linear controller which is located in the feedback loop between a sensing block and a zero-order-hold. The sensing block comprises several sensors with asynchronous uncertain non-uniform sampling intervals. We present sufficient Krasovskii-based stability and stabilization criteria as a set of linear matrix inequalities. It is shown through examples that choosing the right sensors with adequate sampling frequencies has a considerable impact on controller design and stability of the closed-loop system.

Asymptotic stability of sampled-data piecewise affine slab systems

This paper addresses stability analysis of closed-loop sampled-data piecewise affine (PWA) slab systems. In particular, we study the case in which a PWA plant is in feedback with a discrete-time emulation of a PWA controller. We consider the sampled-data system as a continuous-time system with a variable time delay. The contributions of this work are threefold. First, we present a modified Lyapunov-Krasovskii functional (LKF) for studying PWA systems with time delays that is less conservative when compared to previously suggested alternatives. Second, based on the new LKF, sufficient conditions are provided for asymptotic stability of sampled-data PWA slab systems to the origin. These conditions become Linear Matrix Inequalities (LMIs) in the case of a piecewise linear (PWL) controller. Finally, we present an algorithm for finding a lower bound on the maximum delay that preserves asymptotic stability. Therefore, the output of the algorithm provides an upper bound on the minimum sampling frequency that guarantees asymptotic stability of the sampled data system. The new results are successfully applied to a unicycle example.

Piecewise Affine Networked Control Systems

This paper addresses the exponential stability of piecewise affine networked control systems (PWANCS), where a continuous-time piecewise affine (PWA) plant is in feedback with a PWA controller over a communication network. The main contribution of this paper is to propose sufficient Krasovskii-based stability conditions for PWANCS. Furthermore, the problem of finding a lower bound on the maximum network-induced delay that guarantees exponential stability is cast as a convex optimization program in terms of linear matrix inequalities. The network consists of a sample-and-hold device with an unknown and time-varying sampling frequency, and nonideal communication links with data-packet losses and uncertain time-varying communication delays.

Design, construction and fly-by-wireless control of an autonomous Quadrotor helicopter

This paper describes the design, development and analysis of an autonomous Quadrotor Unmanned Aerial Vehicle (UAV) that is controlled using fly-by-wireless technology. A communication protocol between the UAV and a Ground Control Station (GCS) is established to continuously send information from the on-board sensors to the GCS. There, a controller computes the control signal in real-time and sends it back to the UAV to act upon the actuators. An Inertial Measurement Unit (IMU) and a sonar are used as sensors to determine the attitude angles and the height of the UAV, respectively. A state-feedback controller is designed by pole placement. Considering the delays of the wireless network, a Lyapunov-Krasovskii functional is used to determine if the stability of the system is affected by the delay. Some results are presented from initial flight experiments in which attitude angles and altitude are stabilized.

Observer design for linear multi-rate sampled-data systems

This paper addresses observer design for linear systems with multi-rate sampled output measurements. The sensors are assumed to be asynchronous and to have uncertain nonuniform sampling intervals. The contributions of this paper are twofold. Given the maximum allowable sampling period (MASP) for each sensor, the main contribution of the paper is to propose sufficient Krasovskii-based conditions for design of linear observers. The designed observers guarantee exponential convergence of the estimation error to the origin. Most importantly, the sufficient conditions are cast as a set of linear matrix inequalities (LMIs) that can be solved efficiently. As a second contribution, given an observer gain, the problem of finding MASPs that guarantee exponential stability of the estimation error is also formulated as a convex optimization program in terms of LMIs. The theorems are applied to a unicycle path following example.

An Optimal Control Approach to Decentralized Energy-Efficient Coverage Problems

Abstract One of the challenges of working with multi-agent systems is the limited energy of the agents, especially when the agents are flying vehicles with limited batteries to save weight. The main contribution of this paper is to formulate the energy-efficient coverage problem as an optimal control problem. The optimal control problem will be related to Lloyds algorithm. The solution to the optimal control problem is spatially distributed over Delaunay graphs and provides an energy-efficient local controller to maximize the coverage. As a second contribution, by imposing constraints on the parameters of the optimal control problem we guarantee that the agents maintain their energy during the coverage task. As expected, weighting the speed of the agents against the coverage objective will decrease energy consumption in the multi-agent system. Several examples demonstrate the performance of the energy-efficient approach.

An obstruction to solvability of the reach control problem using affine feedback

This paper studies the reach control problem (RCP) using affine feedback on simplices. The contributions of this paper are threefold. First, we identify a new obstruction to solvability of the RCP using affine feedback and provide necessary and sufficient conditions for occurrence of such an obstruction. Second, for two-input systems, these conditions are formulated in terms of scalar linear inequalities. Third, computationally efficient necessary conditions are proposed for checking the obstruction for multi-input systems as feasibility programs in terms of linear inequalities. In contrast to the previous work in the literature, no assumption is imposed on the set of possible equilibria, so the results are applicable to the general RCP.

A convex approach to stabilization of sampled-data piecewise affine slab systems

This paper addresses exponential stability and stabilization of piecewise affine (PWA) slab systems with piecewise linear (PWL) sampled-data feedback. The PWL controller is assumed to be located in the feedback loop between a sampler with an unknown nonuniform sampling rate and a zero-order-hold. Convex Krasovskii-based sufficient conditions are proposed for exponential stability and stabilization of the sampled-data PWA slab system. The main contributions of this paper are twofold. First, the direct sampled-data controller synthesis problem for PWA slab systems is formulated as a convex optimization program with the maximum allowable sampling period as a parameter. Second, sufficient conditions for exponential stability of PWA sampled-data systems are presented. The stability analysis and controller synthesis conditions are cast as linear matrix inequalities. The results are successfully applied to a unicycle path following problem.