l<sup>1</sup> - Optimal-Feedback Controllers for Discrete-Time Systems

Dahleh, Munther A.; Pearson, J.

doi:10.23919/acc.1986.4789245

Cited by 60 publications

(116 citation statements)

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“…Meanwhile, time and especially spatial (trajectory) constrains are crucial for both launch and recovery tasks. The time domain performance can be accounted for directly in the time domain l 1 design (Blanchini & Sznaier, 1994;Dahleh & Pearson, 1987).…”

Section: Robust Modern Controlmentioning

confidence: 99%

Flight Control System Design Optimisation via Genetic Programming

Bourmistrova¹,

Khantsis²

2009

Aerial Vehicles

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Section: Robust Modern Controlmentioning

confidence: 99%

Flight Control System Design Optimisation via Genetic Programming

Bourmistrova¹,

Khantsis²

2009

Aerial Vehicles

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“…Previous work [10,11] used the duality theory for distance problems to arrive at a solution for (OPT). Here we take an alternate approach using Lagrange multiplier theory, which is in fact more intuitive and transparent, to arrive at similar conclusions.…”

Section: Synthesis Of the 41 Controllermentioning

confidence: 99%

“…Since the elements of V* were constructed from zeros inside the unit disc, the entries will eventually decay and only a finite number of the constraints are active. A bound on the number of such constraints can be derived [10]. The problem is now a standard finite-dimensional linear program, which can be solved exactly.…”

Section: Exact Solutions For a Class Of Problemsmentioning

confidence: 99%

“…The 41 problem, formulated in [58], was solved in [10,11]. The theory was further developed in [17,23,24,45,54,55].…”

Section: Introductionmentioning

confidence: 99%

“…Since Dahleh and Pearson ( [10], [11]) presented the solution to the £L optimal control problem, there has been increasing interest in understanding the basic properties of such problems ( [5], [44], [45] and [54]). Considering that in the case of 1'2 and 1,,, optimization ( [20], [65]), state feedback optimal controllers have a very special structure (i.e.…”

Section: Introductionmentioning

confidence: 99%

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Robust Controller Design: Minimizing Peak-to-Peak Gain

Dahleh¹

1992

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A linear matrix inequality approach to peak‐to‐peak gain minimization

Abedor¹,

Nagpal

Poolla

1996

Int. J. Robust Nonlinear Control

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In this paper we take a new approach to the problem of peak-to-peak gain minimization (the L 1 or induced L. problem). This is done in an effort to circumvent the complexity problems of other approaches. Instead of minimizing the induced L. nonn, we minimize the * -norm, the best upper bound on the induced L.nonn obtainable by bounding the reachable set with inescapable ellipsoids. Controller and filter synthesis for * -norm minimization reduces to minimizing a continuous function of a single real variable. This function can be evaluated, in the most complicated case, by solving a Riccati equation followed by an LMI eigenvalue problem. We contend that synthesis is practical now, but a key computational question-is the function to be minimized convex?-remains open. The filters and controllers that result from this approach are at most the same order as the plant, as in the case of LQG and H. design.KEY WORDS peak-to-peak, persistent disturbances, L I , L. J.2. A new approachMotivated by the ideas in the book by Boyd, EI Ghaoui, Feron, and Balakrishnan,'2 we seek to avoid these complexity problems by minimizing the *-norm-an upper bound on the induced L. norm-rather than minimizing the induced L .. norm directly. This upper bound comes from approximating the set of states reachable with norm-bounded input with inescapable ellipsoids, as is done by Schweppe" and by Boyd, et al.'2 It will be shown that the * -norm is the tightest upper bound obtainable by approximating the reachable set with inescapable ellipsoids.In addition, we consider a different signal norm here than the standard L.. norm: at every time instant we take the 2-norm (Euclidean norm) instead of the oo-norm that is used in most of the peak-to-peak literature. This is clarified in the notation section that follows.The filters and controllers that result from this new" approach are comparatively simple; at most they are of the same order as the plant. as in the case of LQG and H. design. Synthesis *Results in the strictly proper case were reported in a conference paper. 14 ~-[*]Thus II Hlli_ is. roughly. the maximum peak-to-peak gain of H. Throughout the paper we use system matrix notation. That is. we abbreviate the finite-dimensional. linear time-invariant (LTI) system i=Ax+Bw. z = Cz +Dwby Here T..., is the transfer function mapping input w to output z, The paper is organized as follows. Section 2 includes an analysis result that can be applied only to strictly proper systems, and the remainder of the section consists of results on filtering. state-feedback control, and output-feedback control. all of which stem from this basic analysis The space of signals L: is defined to be the set of all k-channel signals with finite L_ norm: L~:={v: IIvll_

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l¹ - Optimal-Feedback Controllers for Discrete-Time Systems

Cited by 60 publications

References 0 publications

Flight Control System Design Optimisation via Genetic Programming

Flight Control System Design Optimisation via Genetic Programming

Robust Controller Design: Minimizing Peak-to-Peak Gain

A linear matrix inequality approach to peak‐to‐peak gain minimization

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l1 - Optimal-Feedback Controllers for Discrete-Time Systems

Cited by 60 publications

References 0 publications

Flight Control System Design Optimisation via Genetic Programming

Flight Control System Design Optimisation via Genetic Programming

Robust Controller Design: Minimizing Peak-to-Peak Gain

A linear matrix inequality approach to peak‐to‐peak gain minimization

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Product

Resources

About

l¹ - Optimal-Feedback Controllers for Discrete-Time Systems