120 research outputs found
On generalized terminal state constraints for model predictive control
This manuscript contains technical results related to a particular approach
for the design of Model Predictive Control (MPC) laws. The approach, named
"generalized" terminal state constraint, induces the recursive feasibility of
the underlying optimization problem and recursive satisfaction of state and
input constraints, and it can be used for both tracking MPC (i.e. when the
objective is to track a given steady state) and economic MPC (i.e. when the
objective is to minimize a cost function which does not necessarily attains its
minimum at a steady state). It is shown that the proposed technique provides,
in general, a larger feasibility set with respect to existing approaches, given
the same computational complexity. Moreover, a new receding horizon strategy is
introduced, exploiting the generalized terminal state constraint. Under mild
assumptions, the new strategy is guaranteed to converge in finite time, with
arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal
state constraint, while still enjoying a larger feasibility set. The features
of the new technique are illustrated by three examples.Comment: Part of the material in this manuscript is contained in a paper
accepted for publication on Automatica and it is subject to Elsevier
copyright. The copy of record is available on http://www.sciencedirect.com
On reduction of differential inclusions and Lyapunov stability
In this paper, locally Lipschitz, regular functions are utilized to identify
and remove infeasible directions from set-valued maps that define differential
inclusions. The resulting reduced set-valued map is point-wise smaller (in the
sense of set containment) than the original set-valued map. The corresponding
reduced differential inclusion, defined by the reduced set-valued map, is
utilized to develop a generalized notion of a derivative for locally Lipschitz
candidate Lyapunov functions in the direction(s) of a set-valued map. The
developed generalized derivative yields less conservative statements of
Lyapunov stability theorems, invariance theorems, invariance-like results, and
Matrosov theorems for differential inclusions. Included illustrative examples
demonstrate the utility of the developed theory
Lyapunov Conditions for Input-to-State Stability of Impulsive Systems
This paper introduces appropriate concepts of input-to-state stability (ISS) and integral-ISS for impulsive systems, i.e., dynamical systems that evolve according to ordinary differential equations most of the time, but occasionally exhibit discontinuities (or impulses). We provide a set of Lyapunov-based sufficient conditions for establishing these ISS properties. When the continuous dynamics are ISS but the discrete dynamics that govern the impulses are not, the impulses should not occur too frequently, which is formalized in terms of an average dwell-time (ADT) condition. Conversely, when the impulse dynamics are ISS but the continuous dynamics are not, there must not be overly long intervals between impulses, which is formalized in terms of a novel reverse ADT condition. We also investigate the cases where (i) both the continuous and discrete dynamics are ISS and (ii) one of these is ISS and the other only marginally stable for the zero input, while sharing a common Lyapunov function. In the former case we obtain a stronger notion of ISS, for which a necessary and sufficient Lyapunov characterization is available. The use of the tools developed herein is illustrated through examples from a Micro-Electro-Mechanical System (MEMS) oscillator and a problem of remote estimation over a communication network
Nonholonomic control systems: from steering to stabilization with sinusoids
The authors present a control law for globally asymptotically stabilizing a class of controllable nonlinear systems without drift. The control law combines earlier work in steering nonholonomic systems using sinusoids at integrally related frequencies, with the ideas in recent results on globally stabilizing linear and nonlinear systems through the use of saturation functions. Simulation results for stabilizing a simple kinematic model of an automobile are included
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