652 research outputs found
Mixed-integer optimal control under minimum dwell time constraints
AbstractTailored Mixed-Integer Optimal Control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time (MDT) constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems (MIOCPs) to
ϵ
-optimality by solving one continuous nonlinear program and one mixed-integer linear program (MILP). Within this work, we analyze the integrality gap of MIOCPs under MDT constraints by providing tight upper bounds on the MILP subproblem. We suggest different rounding schemes for constructing MDT feasible control solutions, e.g., we propose a modification of Sum Up Rounding. A numerical study supplements the theoretical results and compares objective values of integer feasible and relaxed solutions
Characterization and Computation of Invariant Sets for Constrained Switched Systems
Ph.DDOCTOR OF PHILOSOPH
Practical dwell times for switched system stability with smart grid application
Switched systems are encountered throughout many engineering disciplines, but confirming their stability is a challenging task. Even if each subsystem is asymptotically stable, certain switching sequences may exist that drive the overall system states into unacceptable regions. This thesis contains a process that grants stability under switching to switched systems with multiple operating points. The method linearizes a switched system about its distinct operating points, and employs multiple Lyapunov functions to produce modal dwell times that yield stability. This approach prioritizes practicality and is designed to be useful for large systems with many states and subsystems due to its ease of algorithmic implementation. Power applications are particularly targeted, and several examples are provided in the included papers that apply the technique to boost converters, electric machines, and smart grid architectures --Abstract, page iv
Online Optimization of LTI Systems Under Persistent Attacks: Stability, Tracking, and Robustness
We study the stability properties of the interconnection of an LTI dynamical
plant and a feedback controller that generates control signals that are
compromised by a malicious attacker. We consider two classes of controllers: a
static output-feedback controller, and a dynamical gradient-flow controller
that seeks to steer the output of the plant towards the solution of a convex
optimization problem. We analyze the stability of the closed-loop system under
a class of switching attacks that persistently modify the control inputs
generated by the controllers. The stability analysis leverages the framework of
hybrid dynamical systems, Lyapunov-based arguments for switching systems with
unstable modes, and singular perturbation theory. Our results reveal that under
a suitable time-scale separation, the stability of the interconnected system
can be preserved when the attack occurs with "sufficiently low frequency" in
any bounded time interval. We present simulation results in a power-grid
example that corroborate the technical findings
Switching tube-based MPC: characterization of minimum dwell-time for feasible and robustly stable switching
We study the problem of characterizing mode dependent dwell-times that guarantee safe and stable operation of disturbed switching linear systems in an MPC framework. We assume the switching instances are not known a-priori, but instantly at the moment of switching. We first characterize dwell-times that ensure feasible and stable switching between independently designed robust MPC controllers by means of the well established exponential stability result available in the MPC literature. Then, we employ the concept of multi-set invariance to improve on our previous results, and obtain an exponential stability guarantee for the switching closed-loop dynamics. The theoretical findings are illustrated via a numerical example
Invariance principles for switched systems with restrictions
In this paper we consider switched nonlinear systems under average dwell time
switching signals, with an otherwise arbitrary compact index set and with
additional constraints in the switchings. We present invariance principles for
these systems and derive by using observability-like notions some convergence
and asymptotic stability criteria. These results enable us to analyze the
stability of solutions of switched systems with both state-dependent
constrained switching and switching whose logic has memory, i.e., the active
subsystem only can switch to a prescribed subset of subsystems.Comment: 29 pages, 2 Appendixe
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