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In this paper, a hysteresis model-based nonlinear robust controller is developed for a piezoelectric actuator, utilizing a Lyapunov-based stability analysis, which ensures that a desired displacement trajectory is accurately tracked.
A networked control framework for linear uncertain systems with input quantization and deadzone is developed via adaptive control approach. The proposed framework is Lyapunov-based and guarantees ultimate boundedness of the closed-loop system. Specifically, the quantizers are logarithmic and characterized by sector-bound conditions with the conic sectors adjusted at each time instant by the adaptive...
This paper investigates the stabilization problem for a class of nonlinear uncertain networked control systems (NCSs) with random communication time-delays. The nonlinear NCSs are described by a set of local linear systems which are combined using a Takagi-Sugeno model. Both sensor-to- controller and controller-to-actuator random network-induced delays are considered. Markov processes are using to...
This paper presents results implementing Lyapunov vector fields for the guidance of unmanned aircraft. The vector fields yield globally stable tracking of circular loiter patterns. These loiter patterns are used in several unmanned aircraft applications including hierarchical micro air vehicle control for cooperative plume tracking, extremum seeking for electronic chaining, and cooperative tracking...
Large engineering systems exist, such as air traffic control and Internet routing, for which resources must be allocated amongst a few competitive agents with significant market power. Lump-sum market mechanisms are attractive for these resource allocation problems because the ability of individual agents to manipulate market prices has been shown to be limited. This work addresses the issue of convergence...
We propose an adaptive output-feedback control design technique for a class of feedforward systems with input-to-state stable (ISS) appended dynamics. The system contains uncertain functions involving all states with the assumed bounds on uncertain functions allowed to contain crossproducts of unknown parameters and unmeasured states. The ISS appended dynamics are coupled with all the system states...
A compensator is proposed to achieve globally and practically adaptive output tracking control for a class of linearly parameterized nonlinear systems with uncontrollable unstable linearization under the framework Immersion and Invariance (I&I) tool. As illustrated in [9], the globally asymptotic output tracking of a time-varying reference signal for this class of nonlinear systems is usually...
We present some new results concerning the stability of positive switched linear systems. In particular, we present a necessary and sufficient condition for the existence of copositive linear Lyapunov functions for switched systems with two constituent linear time-invariant (LTI) systems. We also extend some recent results on quadratic stability for positive switched linear systems.
This paper is concerned with the study of, both local and global, uniform asymptotic stability for general nonlinear and time-varying switched systems. Two concepts of Lyapunov functions are introduced and used to establish uniform Lyapunov stability and uniform global stability. With the help of output functions, an almost bounded output energy condition and a persistent excitation (PE) condition...
Three composite quadratic Lyapunov functions are used for the construction of stabilizing laws for discrete-time switched systems. The three functions include the max of quadratics, the min of quadratics and the convex hull of quadratics. Conditions for stabilization are derived as bilinear matrix inequalities and the convergence rate is optimized via linear matrix inequality (LMI) based tools. Numerical...
In this paper, we extend our previous results on practical asymptotic stabilizability to switched systems consisting of time-varying subsystems. There are two main contributions of the paper. First, we formally introduce the concepts of practical uniform asymptotic stabilizability for such systems. Second, we propose some sufficient conditions for the practical uniform asymptotic stabilizability of...
This paper considers the closed-loop stabilization problem for discrete-time linear switched system. The state variables are assumed to be not accessible so that the feedback strategy hinges on given output variables. The solution of this problem is based on the solution of suitable matrix inequalities for the construction of a full order switched filter and the derivation of the stabilization rule...
A new control strategy for the end- effector trajectory tracking (EETT) of a single flexible link manipulator (SFLM) is introduced. The linear dynamic model of the SFLM is expressed in the singularly perturbed form. To reduce the EETT error, a corrective torque is added to the "computed torque control" command of the rigid link counterpart of the SFLM. This corrective torque is derived based...
This tutorial paper presents comprehensive new techniques for adaptive control of PDE systems. It overviews three design methods - the Lyapunov design, the passive design, and the swapping design and discusses tradeoffs between them. The basic ideas for each design are introduced through benchmark plants with constant unknown coefficients. This is then expanded to PDEs with spatially varying coefficients...
Here, model reduction, based on balanced truncation, of stable and passive systems will be considered. An overview over some of the already existing techniques will be given; Lyapunov balancing, Riccati balancing and Stochastic balancing. Subsequently a novel scheme for positive real balanced truncation will be proposed. This new method is a combination of the already existing Lyapunov balancing and...
In this paper, two controllers are developed for flat multi-input/multi-output nonlinear systems. First, a robust adaptive controller is proposed and proven to yield semi-global asymptotic tracking in the presence of additive disturbances and parametric uncertainty. In addition to guaranteeing an asymptotic output tracking result, it is also proven that the parameter estimate vector is driven to a...
Compartmental system models involve dynamic states whose values are nonnegative. These models are widespread in biological and physiological sciences and play a key role in understanding these processes. In this paper, we develop a direct adaptive control framework for compartmental dynamical systems with exogenous bounded disturbances. The proposed framework is Lyapunov-based and guarantees partial...
In this paper, adaptive variable structure neural control is investigated for a class of uncertain SISO nonlinear systems in a Brunovsky form with state time-varying delays and unknown dead-zone input. The unknown time-varying delay uncertainties are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linearity function outside the...
In this paper, we present a real-time dynamic minmax optimization technique for a class of nonlinear systems operating over finite-time horizon. The technique is suitable for peak minimization and other types of minmax problems that arise in robust control problems. As in MPC, the optimization algorithm is based on the minimization of a cost function whose minimization provides stability to the closed-loop...
In this paper, a repetitive learning control (RLC) approach is proposed for a class of remote control nonlinear systems satisfying the global Lipschitz condition. Since there exist time delays in the two transmission channels, tracking a desired trajectory through a remote controller is not an easy task. In order to solve this problema predictor is designed on the controller side to predict the future...
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