Hoai-Nam Nguyen

Implicit improved vertex control for uncertain, time-varying linear discrete-time systems with state and control constraints

The problem of regulating an uncertain and/or time-varying linear discrete-time system with state and control constraints to the origin is addressed. It is shown that feasibility and a robustly asymptotically stable closed loop can be achieved using an interpolation technique. The design method can be seen as an alternative to optimization-based control schemes such as Robust Model Predictive Control. Especially for problems requiring complex calculations to find the optimal solution, the present method can provide a straightforward suboptimal solution. A simulation demonstrates the performance of this class of constrained controllers.

Improved vertex control for time-varying and uncertain linear discrete-time systems with control and state constraints

This paper addresses the problem of regulating a discrete-time linear uncertain and time-varying system to the origin. It is shown that, based on an interpolation technique, by minimizing an appropriate objective function, how feasibility and a robustly and asymptotically stable closed-loop behavior can be achieved. It is shown that the control is a piecewise afflne and continuous function of the state. Several simulations demonstrate the performance of our results.

Constrained Control of Uncertain, Time-varying Linear Discrete-Time Systems Subject to Bounded Disturbances

The aim of this technical note is twofold. In the first part, robust invariance for ellipsoidal sets with respect to uncertain and/or time-varying linear discrete-time systems with bounded additive disturbances is revisited. We provide an extension of an existing invariance condition. In the second part a novel robust interpolation based control design involving several local unconstrained robust optimal controls is proposed. At each time instant a quadratic programming problem is solved on-line. Proofs of recursive feasibility and input-to-state stability are given.

A patchy approximation of explicit model predictive control

The explicit solution of multi-parametric optimisation problems (MPOP) has been used to construct an off-line solution to relatively small- and medium-sized constrained control problems. The control design principles are based on receding horizon optimisation and generally use linear prediction models for the system dynamics. In this context, it can be shown that the optimal control law is a piecewise linear (PWL) state feedback defined over polytopic cells of the state space. However, as the complexity of the related optimisation problems increases, the memory footprint and implementation of such explicit optimal solution may be burdensome for the available hardware, principally due to the high number of polytopic cells in the state-space partition. In this article we provide a solution to this problem by proposing a patchy PWL feedback control law, which intend to approximate the optimal control law. The construction is based on the linear interpolation of the exact solution at the vertices of a feasible set and the solution of an unconstrained linear quadratic regulator (LQR) problem. With a hybrid patchy control implementation, we show that closed-loop stability is preserved in the presence of additive measurement noise despite the existence of discontinuities at the switch between the overlapping regions in the state-space partition.

An interpolation approach for robust constrained output feedback

In this paper, we consider the regulation problem for uncertain linear discrete time systems with bounded disturbance, bounded input and bounded output. Based on the input-output representation, an extended state space model is constructed via the delayed inputs and outputs of the systems and hence there is no need for any estimate of the unmeasured states. The control is obtained using an interpolation technique, which assures feasibility and a robustly asymptotically stable closed loop behavior.

Experimental validation of a nonlinear mpc strategy for a wave energy converter prototype

One of the major limitations to the development of advanced wave energy converters (WECs) control strategies are the associated computational costs. For instance, model predictive control (MPC) strategies have the potential to obtain almost optimal performance, provided that the imperfect power conversion in the power take-off (PTO) system is correctly taken into account in the optimization criterion and that the incoming wave force can be estimated and forecast. However, demanding computational requirements as well as the unresolved issue of wave force estimation have so far prevented real-time implementation and validation of such MPC strategies. In this paper, we present the successful experimental results obtained on a scaled-down prototype of the well-known Wavestar machine. Performance comparisons are provided for nonlinear MPC versus a reference PI controller. INTRODUCTION A wave energy converter (WEC) is a device used to produce electricity, or other forms of usable energy, from wave motion. The main challenge faced by the developers of wave energy technologies is the reduction of the levelized cost of energy (LCOE) to a competitive level. A key driver to achieve such a goal is the improvement of “wave-to-wire” efficiency, which, especially for point absorbers of the heaving-buoy type, depends on: • their architecture (geometry, mechanics), • the efficiency of the power take-off (PTO) system • the performance of the PTO control system [1]. ∗Address all correspondence to this author. In order to deal with the naturally narrow-banded frequency response of such dynamic systems, and the continuously changing sea state, flexible PTOs capable of both harvesting and drawing power from the grid (respectively in generator and motor modes) are promising actuator candidates. A flexible PTO along with reactive control allows the absorber to be more often in phase with the incoming waves. It can achieve that, by investing some energy (drawn from the grid) to eventually get a larger energy payback than it would be possible to obtain by just braking the absorber via the PTO force. Indeed, many studies have shown that one of the key aspects for maximizing the energy yield of a WEC is the way of controlling the device. The ProportionalIntegral (PI) velocity feedback controller is the current state of the art for WECs as far as practical implementation is concerned. The integral action is a position feedback implementing a simple form of reactive control, while the proportional velocity feedback provides the basic linear damping which is found in most WEC control system. This strategy is very robust and simple to implement, since it uses only position and velocity measurements to compute the control action. The PI control law shows a reasonable energy conversion rate, but is still far below the theoretical optimum discussed in [2]. Moreover, additional performance loss is to be expected because the sea state changes and the feedback coefficients must be modified online to take into account this variation. Of course, alternatives to PI control do exist. Latching control has been proposed for WECs equipped with a position locking mechanism [3–5]. The basic idea is to lock the point absorber when its velocity is zero, and wait for the most favorable moment to release it again. In this way, the velocity of the point absorber can be brought in phase with the wave excitation force, and the

More efficient interpolating control

Recent papers proposed an interpolating control methodology for linear discrete-time systems subject to input and state (output) constraints. The main idea of the approach is to blend a local high-gain optimal controller with a global low-gain vertex controller via interpolation. At each time instant, two linear programming problems of relatively small dimensions are solved online. The approach can be seen as an alternative to optimization based control schemes such as model predictive control. However for high-dimensional systems, computing a feasible set for vertex control is generally challenging, and the ability to determine the feasible set limits the applicability of the approach. The aim of the present paper is to propose a way which removes this difficulty, yields further significant improvements on the computational complexity and on the degree of optimality.

Control with constraints for linear stationary systems: An interpolation approach

We propose a new approach to controlling a discrete linear stationary system with a polyhedral constraint on the state and input. The basic idea is to use interpolation. The control law has both explicit and implicit forms. In the implicit form, at any moment of time, at most two linear programming problems are solved online. In the explicit form, the control law contains piecewise affine and continuous functions of state. This method can be viewed as an alternative to predictive control. We show proofs of recursive realizability and asymptotic stability.

One-step receding horizon control for LPV systems in presence of constraints

This paper proposes a novel receding horizon based controller for LPV discrete-time systems. The main idea exploited in the proposed algorithm is to use a parameter-dependent Lyapunov function together with an interpolation based control approach. At each time instant, the solution is obtained by means of a quadratic programming algorithm. Proofs of recursive feasibility and asymptotic stability are given.

Constrained control of discrete-time linear periodic system

The aim of this paper is twofold. In the first part, we provide a method for constructing invariant sets for discrete-time linear periodic systems with state and input constraints. The main advantage of the method is that it generates invariant sets at any step of the underlying set iteration. In the second part a novel interpolating controller between a local unconstrained optimal control law and a global maximum state contractive controller is proposed. At each time instant, two linear programming problems are solved on-line. Proofs of recursive feasibility and asymptotic stability are given.