Risk-sensitive linear/quadratic/gaussian control

Whittle, Peter

doi:10.1017/s0001867800036508

Cited by 162 publications

(228 citation statements)

References 2 publications

Supporting

Mentioning

227

Contrasting

Order By: Relevance

“…Because some of the timing protocols correspond to nonsequential or 'static' games while others enable sequential choices, equivalence of equilibrium outcomes implies a form of dynamic consistency. Jacobson (1973) and Whittle (1981) first showed that the risk-sensitive control law can be computed by solving a robust penalty problem of the type we have studied here, but without discounting. Subsequent research reconfirmed this link in nonsequential and undiscounted problems, typically posed in nonstochastic environments.…”

Section: Fear Of Model Misspecificationmentioning

confidence: 99%

Robust control and model misspecification

Hansen

Sargent

Turmuhambetova

et al. 2006

Journal of Economic Theory

350

321

View full text Add to dashboard Cite

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.

show abstract

Section: Fear Of Model Misspecificationmentioning

confidence: 99%

Robust control and model misspecification

Hansen

Sargent

Turmuhambetova

et al. 2006

Journal of Economic Theory

350

321

View full text Add to dashboard Cite

show abstract

“…This results in a finite dimensional information state filter, but the static information state feedback control law is calculated off line by (singly not doubly) infinite dimensional dynamic programming equations. Of course, if the plant is additionally linear in the controis, and the index kernel is additionally quadratic in the controls, then this theory leads to known linear quadratic (risk sensitive) controllers [8,20]. These controllers are of course linear and have the same dimension as the plant.…”

Section: Introductionmentioning

confidence: 99%

Finite-dimensional optimal controllers for nonlinear plants

Moore

Baras

1995

Systems & Control Letters

View full text Add to dashboard Cite

Optimal risk sensitive feedback controllers are now available for very general stochastic nonlinear plants and performance indices. They consist of nonlinear static feedback of so called information states from an information state filter. In general, these filters are linear, but infinite dimensional, and the information state feedback gains are derived from (doubly) infinite dimensional dynamic programming. The challenge is to achieve optimal finite dimensional controllers using finite dimensional calculations for practical implementation.This paper derives risk sensitive optimality results for finite-dimensional controllers. The controllers can be conveniently derived for 'linearized' (approximate) models (applied to nonlinear stochastic systems). Performance indices for which the controllers are optimal for the nonlinear plants are revealed. That is, inverse risk-sensitive optimal control results for nonlinear stochastic systems with finite dimensional linear controllers are generated. It is instructive to see from these results that as the nonlinear plants approach linearity, the risk sensitive finite dimensional controllers designed using linearized plant models and risk sensitive indices with quadratic cost kernels, are optimal for a risk sensitive cost index which approaches one with a quadratic cost kernel. Also even far from plant linearity, as the linearized model noise variance becomes suitably large, the index optimized is dominated by terms which can have an interesting and practical interpretation.Limiting versions of the results as the noise variances approach zero apply in a purely deterministic nonlinear Ho~ setting. Risk neutral and continuous-time results are summarized.More general indices than risk sensitive indices are introduced with the view to giving useful inverse optimal control results in non-Gaussian noise environments.

show abstract

“…However, it is only in [2] that the complete solution to this problem was finally obtained. The discrete-time partial observation problem was solved by Whittle in [18] (see also [19]). An important relation with robust controllers was found in [5], [6], whereas the risk-sensitive maximum principle was studied in [14], [15], [8], [10].…”

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

confidence: 99%

“…Assumption 5 There exist unique global solutions P (·) and U (·) to equations (18) and (19), respectively.…”

Section: Assumptionmentioning

confidence: 99%

Generalised Risk-Sensitive Control with Full and Partial State Observation

Date

Gashi

2012

J Math Model Algor

View full text Add to dashboard Cite

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.

show abstract

Risk-sensitive linear/quadratic/gaussian control

Cited by 162 publications

References 2 publications

Robust control and model misspecification

Robust control and model misspecification

Finite-dimensional optimal controllers for nonlinear plants

Generalised Risk-Sensitive Control with Full and Partial State Observation

Contact Info

Product

Resources

About