370 research outputs found
Feedback Stabilization of Nonlinear Systems
No full textWe consider the simplest design problem for nonlinear systems: the problem of rendering asymptotically stable a given equilibrium by means of feedback. For such a problem, we provide a necessary condition, known as Brockett condition, and a sufficient condition, which relies upon the definition of a class of functions, known as control Lyapunov functions. The theory is illustrated by means of a few examples. In addition we discuss a nonlinear enhancement of the so-called separation principle for stabilization by means of partial state information
Distributed Model Predictive Control
No full textDistributed model predictive control refers to a class of predictive control architectures in which a number of local controllers manipulate a subset of inputs to control a subset of outputs (states) composing the overall system. Different levels of communication and (non)cooperation exist, although in general the most compelling properties can be established only for cooperative schemes, those in which all local controllers optimize local inputs to minimize the same plantwide objective function. Starting from state-feedback algorithms for constrained linear systems, extensions are discussed to cover output feedback, reference target tracking, and nonlinear systems. An outlook of future directions is finally presented
Tracking and Regulation in Linear Systems
No full textTracking and regulation refers to the ability of a control system to track/reject a given family of reference/disturbance signals modelled as solutions of a differential/difference equation. The problem can be posed as a stabilization problem with a constraint on the steady-state response of the system. For linear, time-invariant, systems the problem can be solved provided a system of linear matrix equations admits a solution. Properties of this system of equations are discussed, together with a general property of all controllers achieving tracking and regulation: the so-called internal model principle
Robot Teleoperation
No full textRobots may allow human beings to physically interact with remote objects and environments. This possibility is known as robot teleoperation and permits to operate in conditions or environments dangerous for human operators. Although teleoperation was among the first developments in robotics back in the 1950's, still nowadays there are important and difficult challenges for researchers and scientists, showing the intrinsic difficulties of this fascinating field of robotics
Nonlinear Adaptive Control
No full textWe consider the control of nonlinear systems in which parameters are uncertain and may vary. For such systems the control must adapt to the parameter change to deliver closed-loop performance, such as asymptotic stability or tracking. A concise description of available methods and basic adaptive stabilization results, which can be used as building blocks for complex adaptive control problems, are discussed
Stability: Lyapunov, Linear Systems
No full textThe notion of stability allows to study the qualitative behavior of dynamical systems. In particular it allows to study the behavior of trajectories close to an equilibrium point or to a motion. The notion of stability that we discuss has been introduced in 1882 by the Russian mathematician A.M. Lyapunov in his doctoral thesis; hence it is often referred to as Lyapunov stability. In this article we discuss and characterize Lyapunov stability for linear systems
Observers in Linear Systems Theory
No full textObservers are dynamical systems which process the input and output signals of a given dynamical system and deliver an online estimate of the internal state of the system which asymptotically converges to the exact value of the state. For linear, finite-dimensional, time-invariant systems, observers can be designed provided a weak observability property, known as detectability, holds
Realizations in Linear Systems Theory
No full textWhen a state variable description of a linear system is known, then its input–output behavior can be easily realized by interconnecting simpler components. The problem of realization is the inverse of this process and can be formulated as follows: given an input–output description, such as the impulse response or the transfer function in the case of time-invariant systems, find a state variable description the impulse response or transfer function of which is the given one. Existence and minimality conditions are discussed. We are interested in realizations of minimum order, which is the case when the realization is both reachable and observable. Realizations for both continuous-time and discrete-time systems are discussed
Finite-Horizon Linear-Quadratic Optimal Control with General Boundary Conditions
No full textThe linear-quadratic (LQ) problem is the prototype of a large number of optimal control problems, including the fixed endpoint, the point-to-point, and several H2 control problems, as well as the dual counterparts. In the past 50 years, these problems have been addressed using different techniques, each tailored to their specific structure. It is only in the last 10 years that it was recognized that a unifying framework is available. This framework hinges on formulae that parameterize the solutions of the Hamiltonian differential equation in the continuous-time case and the solutions of the extended symplectic system in the discrete-time case. Whereas traditional techniques involve the solutions of Riccati differential or difference equations, the formulae used here to solve the finite-horizon LQ control problem only rely on solutions of the algebraic Riccati equations. In this entry, aspects of the framework are described within a discrete-time context
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