Mean and variance of the LQG cost function

The linear-quadratic-Gaussian (LQG) control paradigm is well-known in literature. The strategy of minimizing the cost function is available, both for the case where the state is known and where it is estimated through an observer. The situation is different when the cost function has an exponential discount factor, also known as a prescribed degree of stability. In this case, the optimal control strategy is only available when the state is known. This paper builds on from that result, deriving an optimal control strategy when working with an estimated state. Expressions for the resulting optimal expected cost are also given.

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“…Our goal is to choose F α and K α so as to minimize the expected cost J. This cost, according to [3,Theorem 2], equals…”

Section: Optimizing the Discounted Cost Functionmentioning

confidence: 99%

Optimal controller/observer gains of discounted-cost LQG systems

Bijl

Schön

2019

Automatica

Self Cite

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“…Usually, the expected value of the cost function is minimized, however, there are also approaches that consider variance such as minimum variance control (see [1] for details). Closed form solutions for the variance of the cost were derived very recently in [15]. Taking this approach one step further, we consider the full distribution of the cost functional.…”

Section: Model-based Design Model Learningmentioning

confidence: 99%

Event-triggered Learning for Linear Quadratic Control

Schlüter,

Solowjow,

Trimpe

2019

Preprint

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When models are inaccurate, performance of modelbased control will degrade. For linear quadratic control, an eventtriggered learning framework is proposed that automatically detects inaccurate models and triggers learning of a new process model when needed. This is achieved by analyzing the probability distribution of the linear quadratic cost and designing a learning trigger that leverages Chernoff bounds. In particular, whenever empirically observed cost signals are located outside the derived confidence intervals, we can provably guarantee that this is with high probability due to a model mismatch. With the aid of numerical and hardware experiments, we demonstrate that the proposed bounds are tight and that the event-triggered learning algorithm effectively distinguishes between inaccurate models and probabilistic effects such as process noise. Thus, a structured approach is obtained that decides when model learning is beneficial.

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“…It is shown that the discounted-cost linear quadratic regulator can not only achieve the prescribed optimization index, but also guarantees the exponential stable of the optimal control system [1]. Therefore, the the discounted-cost linear quadratic regulation problem has attracted increasing attention in recent years, especial for non-switched systems [3,4]. For the linear quadratic Gaussian systems, [4] presented a set of analytic expressions for the mean and variance of the discounted-cost function by Lyapunov equations.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the the discounted-cost linear quadratic regulation problem has attracted increasing attention in recent years, especial for non-switched systems [3,4]. For the linear quadratic Gaussian systems, [4] presented a set of analytic expressions for the mean and variance of the discounted-cost function by Lyapunov equations. [3] proposed the optimal controller and observer gains for a class of the linear quadratic Gaussian systems by solving the Riccati equation.…”

Section: Introductionmentioning

confidence: 99%

Discounted-cost Linear Quadratic Regulation of Switched Linear Systems

Xiang

2021

Preprint

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In this paper, we will investigate the design of discounted-cost linear quadratic regulator for switched linear systems. The distinguishing feature of the proposed method is that the designed discounted-cost linear quadratic regulator will achieve not only the desired optimization index, but also the exponentially convergent of the state trajectory of the closed-loop switched linear systems. First, we adopt the embedding transformation to transform the studied problem into a quadratic-programming problem. Then, the bang-bang-type solution of the embedded optimal control problem on a finite time horizon is the optimal solution to the original problems. The bang-bang-type solutions of the embedded optimal control problem is to be shown the optimization solution of the studied problem. Then, the computable sufficient conditions on discounted-cost linear quadratic regulator are proposed for finite-time and infinite-time horizon case, respectively. Finally, an example is provided to demonstrate the effectiveness of the proposed method.

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Mean and variance of the LQG cost function

Cited by 7 publications

References 13 publications

Optimal controller/observer gains of discounted-cost LQG systems

Optimal controller/observer gains of discounted-cost LQG systems

Event-triggered Learning for Linear Quadratic Control

Discounted-cost Linear Quadratic Regulation of Switched Linear Systems

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