Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games

Jacobson, D. H.

doi:10.1109/tac.1973.1100265

Cited by 626 publications

(367 citation statements)

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“…As the name suggests, the exponentiation inside the expectation makes this objective more sensitive to risky outcomes. Jacobson (1973) and Whittle (1981) initiated risk sensitive optimal control in the context of discrete-time linear-quadratic decision problems. Jacobson and Whittle showed that the risk-sensitive control law can be computed by solving a robust penalty problem of the type we have studied here.…”

Section: Risk-sensitive Controlmentioning

confidence: 99%

Robust control and model misspecification

Hansen

Sargent

Turmuhambetova

et al. 2006

Journal of Economic Theory

351

321

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A decision maker fears that data are generated by a statistical perturbation of an approximating model that is either a controlled diffusion or a controlled measure over continuous functions of time. A perturbation is constrained in terms of its relative entropy. Several different two-player zero-sum games that yield robust decision rules and are related to one another, to the max-min expected utility theory of Gilboa and Schmeidler (1989), and to the recursive risk-sensitivity criterion described in discrete time by Hansen and Sargent (1995). To represent perturbed models, we use martingales on the probability space associated with the approximating model. Alternative sequential and non-sequential versions of robust control theory imply identical robust decision rules that are dynamically consistent in a useful sense.

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Section: Risk-sensitive Controlmentioning

confidence: 99%

Robust control and model misspecification

Hansen

Sargent

Turmuhambetova

et al. 2006

Journal of Economic Theory

351

321

View full text Add to dashboard Cite

show abstract

“…Here the approach is to introduce a new probability measure, under which the control problem (6) is transformed into the standard risk-sensitive control problem of Jacobson [9]. Let θ (t), Z(t), and Z be defined as:…”

Section: Proof Of Theorem 1: the Change Of Measure Methodsmentioning

confidence: 99%

“…Thus, we have transformed the original control problem into the one of minimising (12) subject to (13), which is just the standard risk-sensitive control problem [9], the solutions of which is…”

Section: Proof Of Theorem 1: the Change Of Measure Methodsmentioning

confidence: 99%

“…The optimal control problem of finding u(·) that minimises (2) subject to (1), was introduced by Jacobson in [9]. Assuming full state observation, Jacobson has given a complete solution to this problem.…”

Section: [X (T)qx(t) + U (T)ru(t)]dt (2)mentioning

confidence: 99%

“…Note that due to (7), in general it is no longer necessary for R > 0 as in the classical risk-sensitive control [9]. We introduce the matrices:…”

Section: St (5) (6)mentioning

confidence: 99%

See 2 more Smart Citations

Generalised Risk-Sensitive Control with Full and Partial State Observation

Date

Gashi

2012

J Math Model Algor

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This paper generalises the risk-sensitive cost functional by introducing noise dependent penalties on the state and control variables. The optimal control problems for the full and partial state observation are considered. Using a change of probability measure approach, explicit closed-form solutions are found in both cases. This has resulted in a new risk-sensitive regulator and filter, which are generalisations of the well-known classical results.

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Stochastic Systems

Pasik-Duncan

2017

Wiley Encyclopedia of Electrical and Electronics Engineering

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Stochastic systems are described with emphasis on their use in stochastic control, filtering, and stochastic differential games. Some background is given for the Wiener process, stochastic calculus, and stochastic differential equations. The linear filtering problem is described. Some general notions of stochastic control are given and the linear–quadratic Gaussian control problem is solved. Weighted least‐squares estimation is applied to continuous‐time adaptive control and an adaptive control problem is solved. A solution is given for the linear–quadratic control problem with a general noise process. Stochastic differential games are described and both linear and nonlinear stochastic differential games are explicitly solved by determining optimal control strategies.

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Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games

Cited by 626 publications

References 1 publication

Robust control and model misspecification

Robust control and model misspecification

Generalised Risk-Sensitive Control with Full and Partial State Observation

Stochastic Systems

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