Compositional (In)Finite Abstractions for Large-Scale Interconnected Stochastic Systems

This paper is concerned with a compositional approach for constructing both infinite (reduced-order models) and finite abstractions (a.k.a. finite Markov decision processes (MDPs)) of large-scale interconnected discrete-time stochastic systems. The proposed framework is based on the notion of stochastic simulation functions enabling us to employ an abstract system as a substitution of the original one in the controller design process with guaranteed error bounds. In the first part of the paper, we derive sufficient small-gain type conditions for the compositional quantification of the probabilistic distance between the interconnection of stochastic control subsystems and that of their infinite abstractions. We then construct infinite abstractions together with their corresponding stochastic simulation functions for a particular class of discrete-time nonlinear stochastic control systems. In the second part of the paper, we leverage small-gain type conditions for the compositional construction of finite abstractions. We propose an approach to construct finite MDPs as finite abstractions of concrete models or their reduced-order versions satisfying an incremental input-to-state stability property. We demonstrate the effectiveness of the proposed results by applying our approaches to a fully interconnected network of 20 nonlinear subsystems (totally 100 dimensions). We construct finite MDPs from their reduced-order versions (together 20 dimensions) with guaranteed error bounds on their output trajectories. We also apply the proposed results to a temperature regulation in a circular building and construct compositionally a finite abstraction of a network containing 1000 rooms. We employ the constructed finite abstractions as substitutes to compositionally synthesize policies regulating the temperature in each room for a bounded time horizon.Comment: This work is accepted as a full paper at IEEE Transactions on Automatic Contro

Adding integral action for open-loop exponentially stable semigroups and application to boundary control of PDE systems

The paper deals with output feedback stabilization of exponentially stable systems by an integral controller. We propose appropriate Lyapunov functionals to prove exponential stability of the closed-loop system. An example of parabolic PDE (partial differential equation) systems and an example of hyperbolic systems are worked out to show how exponentially stabilizing integral controllers are designed. The proof is based on a novel Lyapunov functional construction which employs the forwarding techniques

Adaptation and regulation with signal detection implies internal model

This note provides a theorem showing, under suitable technical assumptions, that if a system S adapts to a class of external signals U, in the sense of egulation against disturbances or tracking signals in U, then S must ecessarily contain a subsystem which is capable of generating all the signals in U. It is not assumed that regulation is robust, nor is there a prior requirement for the system to be partitioned into separate plant and controller components. Instead, one assumes that a ``signal detection'' property holds. The result was motivated by questions of adaptation in bacterial chemotaxis, but the general mathematical principle is of wide applicability.Comment: See http://www.math.rutgers.edu/~sontag for related work; to appear in Systems and Control Letter

Numerical homotopy continuation for control and online identification of nonlinear systems: the survey of selected results

The article gives an overview of the parameter numerical continuation methodology applied to setpoint control and parameter identification of nonlinear systems. The control problems for affine systems as well as general (nonaffine) nonlinear systems are considered. Online parameter identification is also presented in two versions: with linear and nonlinear nonconvex parameterization. Simulation results for illustrative examples are shown.Comment: Review of recent results. To be publishe

Adaptation Implies Internal Model

This note provides a simple result showing, under suitable technical assumptions, that if a system S adapts to a class of external signals U, then S must necessarily contain a subsystem which is capable of generating all the signals in U. It is not assumed that regulation is robust, nor is there a prior requirement for the system to be partitioned into separate plant and controller components.Comment: Further work in http://math.rutgers.edu/~sonta

Cooperative Global Robust Stabilization for a Class of Nonlinear Multi-Agent Systems and its Application

This paper studies the cooperative global robust stabilization problem for a class of nonlinear multi-agent systems. The problem is motivated from the study of the cooperative global robust output regulation problem for the class of nonlinear multi-agent systems in normal form with unity relative degree which was studied recently under the conditions that the switching network is undirected and some nonlinear functions satisfy certain growth condition. We first solve the stabilization problem by using the multiple Lyapunov functions approach and the average dwell time method. Then, we apply this result to the cooperative global robust output regulation problem for the class of nonlinear systems in normal form with unity relative degree under directed switching network, and have removed the conditions that the switching network is undirected and some nonlinear functions satisfy certain growth condition.Comment: 9 pages, 1 figure. This paper was submitted to the journal "Automatica

Passivity-based neural network adaptive output feedback control for nonlinear nonnegative dynamical systems

Abstract—The potential clinical applications of adaptive neural network control for pharmacology in general, and anesthesia and critical care unit medicine in particular, are clearly apparent. Specifically, monitoring and controlling the depth of anesthesia in surgery is of particular importance. Nonnegative and compartmental models provide a broad framework for biological and physiological systems, including clinical pharmacology, and are well suited for developing models for closed-loop control of drug administration. In this paper, we develop a neural adaptive output feedback control framework for adaptive set-point regulation of nonlinear uncertain nonnegative and compartmental systems. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the error signals corresponding to the physical system states and the neural network weighting gains. The approach is applicable to nonlinear nonnegative systems with unmodeled dynamics of unknown dimension and guarantees that the physical system states remain in the nonnegative orthant of the state–space for nonnegative initial conditions. Finally, a numerical example involving the infusion of the anesthetic drug midazolam for maintaining a desired constant level of depth of anesthesia for noncardiac surgery is provided to demonstrate the efficacy of the proposed approach. Index Terms—Adaptive control, automated anesthesia, bispectral index (BIS), electroencephalography, exponential passivity, neural networks, nonlinear nonnegative systems, nonnegative control, output feedback. I

Adaptive Observers as Nonlinear Internal Models

This paper shows how the theory of nonlinear adaptive observers can be effectively used in the design of internal models for nonlinear output regulation. The theory substantially enhances the existing results in the context of {\em adaptive} output regulation, by allowing for not necessarily stable zero dynamics of the controlled plant and by weakening the standard assumption of having the steady state control input generated by a linear system.Comment: 20 page

Analysis and Control of Period-Doubling Bifurcation in Buck Converters Using Harmonic Balance

Period doubling bifurcation in buck converters is studied by using the harmonic balance method. A simple dynamic model of a buck converter in continuous conduction mode under voltage mode or current mode control is derived. This model consists of the feedback connection of a linear system and a nonlinear one. An exact harmonic balance analysis is used to obtain a necessary and sufficient condition for a period doubling bifurcation to occur. If such a bifurcation occurs, the analysis also provides information on its exact location. Using the condition for bifurcation, a feedforward control is designed to eliminate the period doubling bifurcation. This results in a wider range of allowed source voltage, and also in improved line regulation.Comment: Published in the International Journal of Latin American Applied Research, 31(3), pp. 149-156, Jul. 2001, Special theme issue: Bifurcation Control: Methodologies and Applications, In Honor of the 65th Birthday of Professor Leon O. Chu

Adaptive Semiglobal Nonlinear Output Regulation:An Extended-State Observer Approach

This paper proposes a new extended-state observer-based framework for adaptive nonlinear regulator design of a class of nonlinear systems, in the general nonequilibrium theory. By augmenting an extended-state observer with an internal model, one is able to obtain an estimate of the term containing uncertain parameters, which then makes it possible to design an adaptive internal model in the presence of a general nonlinearly parameterized immersion condition.Comment: 8 pages and 3 figure