11,269 research outputs found
Optimal Switching for Hybrid Semilinear Evolutions
We consider the optimization of a dynamical system by switching at discrete
time points between abstract evolution equations composed by nonlinearly
perturbed strongly continuous semigroups, nonlinear state reset maps at mode
transition times and Lagrange-type cost functions including switching costs. In
particular, for a fixed sequence of modes, we derive necessary optimality
conditions using an adjoint equation based representation for the gradient of
the costs with respect to the switching times. For optimization with respect to
the mode sequence, we discuss a mode-insertion gradient. The theory unifies and
generalizes similar approaches for evolutions governed by ordinary and delay
differential equations. More importantly, it also applies to systems governed
by semilinear partial differential equations including switching the principle
part. Examples from each of these system classes are discussed
Robust Stability Analysis of Nonlinear Hybrid Systems
We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems
Identification of Piecewise Linear Models of Complex Dynamical Systems
The paper addresses the realization and identification problem or a subclass
of piecewise-affine hybrid systems. The paper provides necessary and sufficient
conditions for existence of a realization, a characterization of minimality,
and an identification algorithm for this subclass of hybrid systems. The
considered system class and the identification problem are motivated by
applications in systems biology
Forward Invariant Cuts to Simplify Proofs of Safety
The use of deductive techniques, such as theorem provers, has several
advantages in safety verification of hybrid sys- tems; however,
state-of-the-art theorem provers require ex- tensive manual intervention.
Furthermore, there is often a gap between the type of assistance that a theorem
prover requires to make progress on a proof task and the assis- tance that a
system designer is able to provide. This paper presents an extension to
KeYmaera, a deductive verification tool for differential dynamic logic; the new
technique allows local reasoning using system designer intuition about per-
formance within particular modes as part of a proof task. Our approach allows
the theorem prover to leverage for- ward invariants, discovered using numerical
techniques, as part of a proof of safety. We introduce a new inference rule
into the proof calculus of KeYmaera, the forward invariant cut rule, and we
present a methodology to discover useful forward invariants, which are then
used with the new cut rule to complete verification tasks. We demonstrate how
our new approach can be used to complete verification tasks that lie out of the
reach of existing deductive approaches us- ing several examples, including one
involving an automotive powertrain control system.Comment: Extended version of EMSOFT pape
Switched networks and complementarity
A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise-linear elements, including diodes. We show that the linear complementarity formulation, which already has proved effective for piecewise-linear networks, can be extended in a natural way to also cover switching circuits. To achieve this, we use a generalization of the linear complementarity problem known as the cone-complementarity problem. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we show that within our framework, energy cannot increase as a result of a jump, and we derive a stability result from this
On Weak Topology for Optimal Control of Switched Nonlinear Systems
Optimal control of switched systems is challenging due to the discrete nature
of the switching control input. The embedding-based approach addresses this
challenge by solving a corresponding relaxed optimal control problem with only
continuous inputs, and then projecting the relaxed solution back to obtain the
optimal switching solution of the original problem. This paper presents a novel
idea that views the embedding-based approach as a change of topology over the
optimization space, resulting in a general procedure to construct a switched
optimal control algorithm with guaranteed convergence to a local optimizer. Our
result provides a unified topology based framework for the analysis and design
of various embedding-based algorithms in solving the switched optimal control
problem and includes many existing methods as special cases
- …