Linear controller design: limits of performance via convex optimization

Boyd, Stephen; Baratt, C.; Norman, Stephen A.

doi:10.1109/5.52229

Cited by 159 publications

(174 citation statements)

References 68 publications

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“…We test the proposed method on the problem described in Section 4.3 where the plant is described by (25) and where the nominal controller is described by (26) and (27). The decay rate of the closed-loop system is the minimum value of for which there exists matrices P and D that satisfy is expressed with 40 bits, requiring a total of 1800 bits, i.e.…”

Section: Numerical Instancementioning

confidence: 99%

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Controller coefficient truncation using Lyapunov performance certificate

Skaf

Boyd

2010

Intl J Robust & Nonlinear

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SUMMARYWe describe a method for truncating the coefficients of a linear controller while guaranteeing that a given set of relaxed performance constraints is met. Our method sequentially and greedily truncates individual coefficients, using a Lyapunov certificate, typically in linear matrix inequality (LMI) form, to guarantee the performance. Numerical examples show that the method is surprisingly effective at finding controllers with aggressively truncated coefficients, which meet typical performance constraints. We give an example showing that how the basic method can be extended to handle nonlinear plants and controllers.

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Section: Numerical Instancementioning

confidence: 99%

“…For more on representing control system specifications via LMIs, see, e.g. [24][25][26]. For a given ∈ C, we compute a value of such that L( , ) 0.…”

Section: Interval Computation Via Lyapunov Performance Certificatementioning

confidence: 99%

Controller coefficient truncation using Lyapunov performance certificate

Skaf

Boyd

2010

Intl J Robust & Nonlinear

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“…The parameters α and β can be chosen according to desired design specifications in terms of raise time T s and steady state error which, characterize the time response to unit step inputs [10].…”

Section: Feedback-linearizing Controlmentioning

confidence: 99%

Autocalibrated Gravity Compensation for 3DoF Impedance Haptic Devices

Formaglio

Fei

Mulatto

et al. 2008

Lecture Notes in Computer Science

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Abstract. The apparent mass of haptic device end-effector depends on its position inside the workspace. This paper presents a recursive algorithm to detect effective direction of gravity force, and to automatically estimate the apparent mass of the end-effector when placed at the vertices of a cubic grid contained into the device workspace. Then an on-line technique is proposed to actively compensate gravity, exploiting trilinear interpolation to compute an estimate of end-effector apparent mass in any position of the workspace. Experiments have been performed with three different haptic devices, and results shown that the apparent mass of the end-effector is compensated almost homogeneously with respect to its position in the workspace.

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“…where G zqi is the ith column of the transfer matrix G zq , and · denotes the L 2 norm (see [BB91,§5.2.3]). We can use V q as a measure of the effect of quantization on the overall system performance.…”

Section: Performance Of the Closed-loop Systemmentioning

confidence: 99%

Joint Optimization of Wireless Communication and Networked Control Systems

Xiao

Johansson

Hindi

et al. 2005

Switching and Learning in Feedback Systems

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Abstract. We consider a linear system, such as an estimator or a controller, in which several signals are transmitted over wireless communication channels. With the coding and medium access schemes of the communication system fixed, the achievable bit rates are determined by the allocation of communications resources such as transmit powers and bandwidths, to different channels. Assuming conventional uniform quantization and a standard white-noise model for quantization errors, we consider two specific problems. In the first, we assume that the linear system is fixed and address the problem of allocating communication resources to optimize system performance. We observe that this problem is often convex (at least, when we ignore the constraint that individual quantizers have an integral number of bits), hence readily solved. We describe a dual decomposition method for solving these problems that exploits the problem structure. We briefly describe how the integer bit constraints can be handled, and give a bound on how suboptimal these heuristics can be. The second problem we consider is that of jointly allocating communication resources and designing the linear system in order to optimize system performance. This problem is in general not convex. We present an iterative heuristic method based on alternating convex optimization over subsets of variables, which appears to work well in practice.

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Linear controller design: limits of performance via convex optimization

Cited by 159 publications

References 68 publications

Controller coefficient truncation using Lyapunov performance certificate

Controller coefficient truncation using Lyapunov performance certificate

Autocalibrated Gravity Compensation for 3DoF Impedance Haptic Devices

Joint Optimization of Wireless Communication and Networked Control Systems

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