Authors:
Alberto Bemporad,
Lorenzo Giovanardi,
Fabio D. Torrisi,
Volume: 1, Page 969 Paper number 1844
Abstract:
In this paper we tackle the optimal control problem for piecewise linear
and hybrid systems by using a computational approach based on performance-driven
reachability analysis. The idea consists of coupling a reach-set exploration
algorithm, essentially based on repetitive use of linear programming,
to a quadratic programming solver which selectively drives the exploration.
In particular, an upper bound on the optimal cost is continually updated
during the procedure, and used as a criterion to discern non-optimal
evolutions and to prevent their exploration. The result is an efficient
strategy of branch-and-bound nature, which is especially attractive
for solving long-horizon hybrid optimal control and scheduling problems.
Authors:
Young C. Cho,
Christos G. Cassandras,
David L. Pepyne,
Volume: 1, Page 975 Paper number 1736
Abstract:
This paper considers optimal control problems for a class of hybrid
systems motivated by the structure of manufacturing environments that
integrate process and operations control. We derive new necessary and
sufficient conditions that allow us to determine the structure of the
optimal sample path and hence decompose a large non-convex, non-differentiable
problem into a set of smaller convex, constrained optimization problems.
Using these conditions, we develop an efficient, low-complexity, scalable
algorithm for explicitly determining the optimal controls. Several
numerical examples are included to illustrate the efficacy of the proposed
algorithm.
Authors:
Ekaterina S. Lemch,
Shankar Sastry,
Peter E. Caines,
Volume: 1, Page 981 Paper number 1800
Abstract:
In this paper we investigate the question of the global controllability
posed for a class of control hybrid systems. New sufficient conditions
for the global controllability are obtained in terms of the so-called
hybrid fountains. The main tool for our analysis is the notion of a
controlled hybrifold.
Authors:
Zhenyu Yang,
Volume: 1, Page 987 Paper number 1366
Abstract:
This paper discusses the verification problem of Redundancy Management
Systems (RMS) in fault-tolerant control by using a hybrid system approach
- the Discrete-Event-System (DES) abstracting strategy. The qualitative
fault-tolerant criteria can be formally verified if a DES model is
abstracted from the continuous/discrete-time dynamical system in a
consistent way. In this paper the acquisition of the DES model and
verification of fault-tolerant criteria are illustrated based on a
concrete RMS of a redundant flight control system.
Authors:
Nicola Elia,
Volume: 1, Page 993 Paper number 2128
Abstract:
In this paper we show that, for a linear system, any worst-case energy
gain greater than the optimal H_(infinity) norm is achievable by a
logarithmically quantized state feedback. We also show how to derive
the coarsest logarithmic quantizer provable via quadratic Lyapunov
functions for a given level of performance. The smallest logarithmic
base, for a given performance level, is obtained via a bisection algorithm
applied to a parametric feasibility LMI problem. The result highlights
the tradeoff between performance degradation versus coarseness of
quantization. Simulations suggest that the upper bound derived in
this paper is a realistic measure of the actual performance under logarithmic
quantization. The end result is the systematic design of a discrete
event controller that stabilizes a linear system and guarantees a certain
level of performance measured in terms of the worst-case close loop
energy gain. The resulting hybrid system is implicitly verified.
Authors:
Norihiko Shishido,
Claire J. Tomlin,
Volume: 1, Page 999 Paper number 2182
Abstract:
Verification of safety properties for continuous, discrete, and hybrid
systems requires computation of the reachable sets of states for such
systems. It is of great interest to develop efficient and scalable
numerical algorithms for computation and representation of this reachable
set. In this paper, we compute reachable sets for linear differential
games, in which one player (the `control') tries to keep the state
of the system outside of a given unsafe subset of the state space;
and the second player (the `disturbance') tries to push the system
into this subset. We model this unsafe set, the input set, and the
disturbance set as ellipsoids, and we derive conditions under which
the reachable set at each point in time is an ellipsoid. We give an
integral form equation whose solution represents this ellipsoid, and
we present special cases in which this ellipsoid may be computed analytically.
We conclude with a set of examples.
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