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Variation paradigm is introduced for stability in terms of asymptotic gain of persistent dwell-time switched time-delay systems. The principle of small-variation small-state is conceived to formulate conditions on ultimate variations between end times of dwell-time switching intervals for convergence in these intervals. Trajectory convergence is then derived using evolutionary data in both retarded...
Receding horizon control (RHC) or model predictive control (MPC) solves online a finite horizon open-loop optimal control problem repeatedly in an infinite horizon context and provides a suboptimal control solution. It has been widely used in industry. For continuous-time (CT) systems, two categories of RHC have been investigated in literature, namely instantaneous RHC and sampled-data RHC. This paper...
This paper proposes a method to estimate the region of attraction of nonlinear polynomial systems. Based on quadratic Lyapunov functions, stability analysis conditions in a ??quasi??-LMI form are stated in a regional (local) context. An LMI-based optimization problem is then derived for computing the Lyapunov matrix maximizing the estimate of the region of attraction of the origin.
A new type of global stability is introduced and its equivalent Lyapunov characterization is presented. The problem of global stability of the compact set composed by all invariant solutions of a nonlinear system (several equilibriums, for instance) is analyzed. Consideration of such set allows us to present global stability properties for multi-stable systems.
Interconnection of several hybrid input-to-state stable (ISS) systems is considered in this paper. We ask under what condition is such an interconnection stable and how an ISS-Lyapunov function can be constructed for the whole interconnection. Small-gain condition to assure stability is given. A construction of an ISS-Lyapunov function for the whole system is provided under the small-gain condition.
This paper deals with stabilization of networked control systems (NCS) affected by uncertain time-varying delays and data packet dropouts. We point out that such network effects are likely to render the classical control Lyapunov function (CLF) method unfeasible, mainly due to the monotonic decreasing condition. To solve this problem we make use of a discrete-time equivalent of a control Lyapunov-Razumikhin...
We consider networks of input-to-state dynamically stable (ISDS) systems and provide a small gain condition under which the entire network is again ISDS. A Lyapunov formulation of the nonlinear small gain theorem for two interconnected ISDS systems is proved. It provides a constructive method to find an ISDS Lyapunov function for such an interconnection.
This paper extends the nonlinear ISS small-gain theorem to a large-scale time delay system composed of three or more subsystems. En route to proving this small-gain theorem for systems of differential equations with delays, a small-gain theorem for operators is examined. The result developed for operators allows applications to a wide class of systems, including state space systems with delays.
A recent paper proposed an MPC methodology which achieved a considerable reduction in the online optimization by transferring some of the computational load to calculations that can be performed offline. The approach was based on an augmented autonomous state space formulations of the prediction dynamics and gained significantly in efficiency by imposing a terminal constraint at current time. The...
This paper develops semistability analysis results for nonlinear switched systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. The main results of the paper involve sufficient conditions for semistability using multiple Lyapunov functions and integral-type inequalities.
Commonly, controllers for Linear Parameter- Varying (LPV) systems are designed in continuous-time using a Linear Fractional Representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a discrete-time model of the plant which is often derived from continuous-time first-principle models. Existing...
This paper investigates an event condition for event-driven controllers based on Lyapunov functions. Considering that constant values of a Lyapunov function define contour curves that form closed regions around the equilibrium point, in this paper we present a sampling mechanism that enforces job executions (sampling, control algorithm computation and actuation) each time the system trajectory reaches...
Previous inverse optimal adaptive controllers (IOACs) have been developed that can handle structured (i.e., linear in the parameters (LP)) uncertainty for a particular class of nonlinear systems. A full-state feedback IOAC is developed in the companion Part I paper for Euler-Lagrange systems with an uncertain time varying inertia matrix. In this paper, an output feedback IOAC is developed to asymptotically...
In this work, we focus on the problem of stabilization of two constrained linear systems coupled through the inputs by two different agents which communicate in order to take a decision assuming that each agent only has partial information of the model and the state of the system. We extend previous results on distributed model predictive control and provide sufficient conditions that guarantee practical...
This paper studies a non-linear, discrete-time, matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behaviour. The problem of partial stability, which requires that a specific component of the state of the system converges exponentially, is studied and solved. The convergent state...
This paper considers networks consisting of integral input-to-state stable (iISS) subsystems and addresses the problem of verifying iISS property of a given network. First, we focus on construction of continuously differentiable Lyapunov functions, and derive a condition ensuring the iISS of the network comprising n subsystems. Although this approach referred to as the sum-type construction has not...
Particle swarm optimization (PSO) is an effective robust and simple method to solve many problems proposed in science and engineering. How does the particle motion and how the particles in a swarm find the optimal solutions are an open problem. This paper investigates the particle trajectories for the standard PSO based on difference equations theories. Equilibrium point and asymptotically stable...
This paper considers a swarm model with a class of simple attraction and repulsion functions and delves into the question of ??soft control?? for swarms system in Euclidean space, which disturb the collective behavior of the group by adding a few controlled intelligent agents at the condition of keeping the local rules of the existing agents in the system. This paper gives a control law for controlled...
An adaptive controller for a class of unknown nonaffine discrete-time plants is introduced in this article. The proposed control law is constructed by the estimated system linearization with adjustable networks called Muti-input Fuzzy Rules Emulated Networks or MIFRENs. Only on-line learning phase, the bounded parameters inside MIFRENs and the boundary of control error are given by the proposed theorem...
We consider a system consisting of N parallel queues, served by one server. Time is slotted, and the server serves one of the queues in each time slot, according to some scheduling policy. In the first part of the paper, we characterize the buffer overflow exponents and the likeliest overflow trajectories under the Longest Queue First (LQF) scheduling policy. Under statistically identical arrivals...
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