Linear offset-free Model Predictive Control

This work addresses the problem of offset-free Model Predictive Control (MPC) when tracking an asymptotically constant reference. In the first part, compact and intuitive conditions for offset-free MPC control are introduced by using the arguments of the internal model principle. In the second part, we study the case where the number of measured variables is larger than the number of tracked variables. The plant model is augmented only by as many states as there are tracked variables, and an algorithm which guarantees offset-free tracking is presented. In the last part, offset-free tracking properties for special implementations of MPC schemes are briefly discussed.     

Suppressing intersample behavior in iterative learning control

Iterative Learning Control (ILC) is a control strategy to improve the performance of digital batch repetitive processes. Due to its digital implementation, discrete time ILC approaches do not guarantee good intersample behavior. In fact, common discrete time ILC approaches may deteriorate the intersample behavior, thereby reducing the performance of the sampled-data system. In this paper, a generally applicable multirate ILC approach is presented that enables to balance the at-sample performance and the intersample behavior. Furthermore, key theoretical issues regarding multirate systems are addressed, including the time-varying nature of the multirate ILC setup. The proposed multirate ILC approach is shown to outperform discrete time ILC in realistic simulation examples.     

Optimal dynamic advertising with an adverse exogenous effect on brand goodwill

We propose the model of a firm that advertises a product in a homogeneous market, where a constant exogenous interference is present. Using the framework of Nerlove and Arrow’s advertising model, we assume that the interference acts additively on goodwill production as a negative term. Hence, we allow that the goodwill may become negative and we associate a zero demand with negative goodwill values. We consider a piecewise linear demand function and formulate a nonsmooth optimal-control problem with an infinite horizon. We obtain that an optimal advertising policy exists and takes one of two forms: either a positive and constant advertising effort, or a decreasing effort starting from a positive level and eventually reaching the zero value at a finite exit time. In the former scenario, the demand is always positive and the firm stays in the market in the long run; in the latter, the demand becomes zero in the short run, and afterward, the firm goes out of business. In both cases we have an explicit representation of the optimal control, which is obtained through the study of an auxiliary smooth optimal-control problem. It is interesting that the fundamental choice between staying in the market and going out of business at some time depends both on the interference level and on the initial goodwill level.     

Near optimal interval observers bundle for uncertain bioreactors

In this paper we design an interval observer for the estimation of unmeasured variables of uncertain bioreactors. The observer is based on a bounded error observer, as proposed in [Lemesle, V., & Gouzé, J.-L. (2005). Hybrid bounded error observers for uncertain bioreactor models. Bioprocess and Biosystems Engineering, 27, 311-318], that makes use of a loose approximation of the bacterial kinetics. We first show how to generate guaranteed upper and lower bounds on the state, provided that known intervals for the initial condition and the uncertainties are available. These so-called framers depend on a tuning gain. They can be run in parallel and the envelope provides the best estimate. An optimality criterion is introduced leading to the definition of an optimal observer. We show that this criterion provides directly a gain set containing the best framers. The method is applied to the estimation of the total biomass of an industrial wastewater treatment plant, demonstrating its efficiency.     

A discrete delay decomposition approach to stability of linear retarded and neutral systems

This paper is concerned with stability of linear time-delay systems of both retarded and neutral types by using some new simple quadratic Lyapunov-Krasovskii functionals. These Lyapunov-Krasovskii functionals consist of two parts. One part comes from some existing Lyapunov-Krasovskii functionals employed in [Han, Q.-L. (2005a). Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica, 41, 2171-2176; Han, Q.-L. (2005b). A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices. International Journal of Systems Science, 36, 469-475]. The other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments. Then using these new simple quadratic Lyapunov-Krasovskii functionals, some new discrete delay-dependent stability criteria are derived for both retarded systems and neutral systems. It is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in Han (2005a) and Han (2005b) cited above, respectively. Numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results.     

Observer-based networked control for continuous-time systems with random sensor delays

This paper is concerned with the networked control system design for continuous-time systems with random measurement, where the measurement channel is assumed to subject to random sensor delay. A design scheme for the observer-based output feedback controller is proposed to render the closed-loop networked system exponentially mean-square stable with H_∞ performance requirement. The technique employed is based on appropriate delay systems approach combined with a matrix variable decoupling technique. The design method is fulfilled through solving linear matrix inequalities. A numerical example is used to verify the effectiveness and the merits of the present results.     

Barrier Lyapunov Functions for the control of output-constrained nonlinear systems

In this paper, we present control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint. To prevent constraint violation, we employ a Barrier Lyapunov Function, which grows to infinity when its arguments approach some limits. By ensuring boundedness of the Barrier Lyapunov Function in the closed loop, we ensure that those limits are not transgressed. Besides the nominal case where full knowledge of the plant is available, we also tackle scenarios wherein parametric uncertainties are present. Asymptotic tracking is achieved without violation of the constraint, and all closed loop signals remain bounded, under a mild condition on the initial output. Furthermore, we explore the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions. We also compare our control with one that is based on a Quadratic Lyapunov Function, and we show that our control requires less restrictive initial conditions. A numerical example is provided to illustrate the performance of the proposed control.     

Event-driven optimization-based control of hybrid systems with integral continuous-time dynamics

In this paper we introduce a class of continuous-time hybrid dynamical systems called integral continuous-time hybrid automata (icHA) for which we propose an event-driven optimization-based control strategy. Events include both external actions applied to the system and changes of continuous dynamics (mode switches). The icHA formalism subsumes a number of hybrid dynamical systems with practical interest, e.g., linear hybrid automata. Different cost functions, including minimum-time and minimum-effort criteria, and constraints are examined in the event-driven optimal control formulation. This is translated into a finite-dimensional mixed-integer optimization problem, in which the event instants and the corresponding values of the control input are the optimization variables. As a consequence, the proposed approach has the advantage of automatically adjusting the attention of the controller to the frequency of event occurrence in the hybrid process. A receding horizon control scheme exploiting the event-based optimal control formulation is proposed as a feedback control strategy and proved to ensure either finite-time or asymptotic convergence of the closed-loop.     

Spacecraft relative rotation tracking without angular velocity measurements

We present a solution to the problem of tracking relative rotation in a leader-follower spacecraft formation using feedback from relative attitude only. The controller incorporates an approximate-differentiation filter to account for the unmeasured angular velocity. We show uniform practical asymptotic stability (UPAS) of the closed-loop system. For simplicity, we assume that the leader is controlled and that we know orbital perturbations; however, this assumption can be easily relaxed to boundedness without degrading the stability property. We also assume that angular velocities of spacecraft relative to an inertial frame are bounded. Simulation results of a leader-follower spacecraft formation using the proposed controller structure are also presented.     

Detectability and observability of discrete-time stochastic systems and their applications

This paper studies detectability and observability of discrete-time stochastic linear systems. Based on the standard notions of detectability and observability for time-varying linear systems, corresponding definitions for discrete-time stochastic systems are proposed which unify some recently reported detectability and exact observability concepts for stochastic linear systems. The notion of observability leads to the stochastic version of the well-known rank criterion for observability of deterministic linear systems. By using these two concepts, the discrete-time stochastic Lyapunov equation and Riccati equations are studied. The results not only extend some of the existing results on these two types of equation but also indicate that the notions of detectability and observability studied in this paper take analogous functions as the usual concepts of detectability and observability in deterministic linear systems. It is expected that the results presented may play important roles in many design problems in stochastic linear systems.