4,011 research outputs found
Robust Constrained Model Predictive Control using Linear Matrix Inequalities
The primary disadvantage of current design techniques for model predictive control (MPC) is their inability to deal explicitly with plant model uncertainty. In this paper, we present a new approach for robust MPC synthesis which allows explicit incorporation of the description of plant uncertainty in the problem formulation. The uncertainty is expressed both in the time domain and the frequency domain. The goal is to design, at each time step, a state-feedback control law which minimizes a "worst-case" infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques, the problem of minimizing an upper bound on the "worst-case" objective function, subject to input and output constraints, is reduced to a convex optimization involving linear matrix inequalities (LMIs). It is shown that the feasible receding horizon state-feedback control design robustly stabilizes the set of uncertain plants under consideration. Several extensions, such as application to systems with time-delays and problems involving constant set-point tracking, trajectory tracking and disturbance rejection, which follow naturally from our formulation, are discussed. The controller design procedure is illustrated with two examples. Finally, conclusions are presented
Performance Control for Interconnection of Identical Systems: Application to PLL network design
International audienceIn this paper, the problem of the control law design for interconnected identical systems ensuring the global stability and the global performance properties is under consideration. Inspired by the decentralized control law design methodology using the dissipativity input–output approach, the problem is reduced to the problem of satisfying two conditions: (i) the condition on the interconnection and (ii) the condition on the local subsystem dynamics. Both problems are efficiently solved applying a (quasi‐) convex LMI optimization and standard H∞ synthesis. The proposed design methodology is applied to the control law design of a synchronous PLL network
dtControl: Decision Tree Learning Algorithms for Controller Representation
Decision tree learning is a popular classification technique most commonly
used in machine learning applications. Recent work has shown that decision
trees can be used to represent provably-correct controllers concisely. Compared
to representations using lookup tables or binary decision diagrams, decision
trees are smaller and more explainable. We present dtControl, an easily
extensible tool for representing memoryless controllers as decision trees. We
give a comprehensive evaluation of various decision tree learning algorithms
applied to 10 case studies arising out of correct-by-construction controller
synthesis. These algorithms include two new techniques, one for using arbitrary
linear binary classifiers in the decision tree learning, and one novel approach
for determinizing controllers during the decision tree construction. In
particular the latter turns out to be extremely efficient, yielding decision
trees with a single-digit number of decision nodes on 5 of the case studies
Robust nonlinear control of vectored thrust aircraft
An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations
Robust Fixed-Order Controller Design with Common Lyapunov Strictly Positive Realness Characterization
This paper investigates the design of a robust fixed-order controller for a
polytopic system with interval uncertainties, with the aim that the closed-loop
stability is appropriately ensured and the performance specifications on
sensitivity shaping are conformed in a specific finite frequency range.
Utilizing the notion of common Lyapunov strictly positive realness
(CL-SPRness), the equivalence between strictly positive realness (SPRness) and
strictly bounded realness (SBRness) is elegantly established; and then the
specifications on robust stability and performance are transformed into the
SPRness of newly constructed systems and further characterized in the framework
of linear matrix inequality (LMI) conditions. Compared with the traditional
robust controller synthesis approaches, the proposed methodology here avoids
the tedious yet mandatory evaluations of the specifications on all vertices of
the polytopic system; only a one-time checking of matrix existence is needed
exclusively, and thus the typically heavy computational burden involved (in
such robust controller design problems) is considerably alleviated. Moreover,
it is noteworthy that the proposed methodology additionally provides essential
necessary and sufficient conditions for this robust controller design with the
consideration of a prescribed finite frequency range; and therefore
significantly less conservatism is attained in the system performance.Comment: 10 pages, 6 figure
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