Optimal control of partially observable discrete time stochastic hybrid systems for safety specifications

Ding, Jerry; Abate, Alessandro; Tomlin, Claire J.

doi:10.1109/acc.2013.6580815

Cited by 18 publications

(37 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The belief state we derived in [8] is closely related to the one derived in [7]. The authors of [7] introduce a binary variable to the state space that represents whether or not the state of the system has remained within K until the previous time step, and generate a belief state that is a joint probability distribution over the current state of the system plus the binary variable.…”

Section: B Dynamic Programming Solutionmentioning

confidence: 98%

“…the system is partially observable, viability analysis is even more difficult, both computationally and theoretically. While some work has been done on deterministic systems with imperfect but non-stochastic measurements [5], [6], and theoretical results have been recently established for partially observable stochastic hybrid systems [7], [8], almost no feasible numerical techniques exist for solving viability problems in the presence of stochastic measurements.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computing probabilistic viable sets for partially observable systems using truncated gaussians and adaptive gridding

Lesser

Oishi

2015

2015 American Control Conference (ACC)

View full text Add to dashboard Cite

We consider the problem of probabilistic safety verification and controller synthesis for linear time-invariant (LTI) systems with noisy state measurements. Almost no numerical results are available for safety verification of partially observable systems. We model the problem as an equivalent optimal control problem over a belief state that is a modified conditional probability density of the current state of the system. The belief state is shown to be a truncated Gaussian density in the case of LTI systems with Gaussian measurement noise, and a novel algorithm is proposed that extends existing pointbased solvers to include the truncated Gaussian belief state, and continuous observation space that is adaptively gridded to reduce estimation error and increase speed of computation. Preliminary results show the method to be promising in terms of computation time as compared to other approaches.

show abstract

Section: B Dynamic Programming Solutionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Computing probabilistic viable sets for partially observable systems using truncated gaussians and adaptive gridding

Lesser

Oishi

2015

2015 American Control Conference (ACC)

View full text Add to dashboard Cite

show abstract

“…But there are only a few works on stochastic hybrid systems with partial information. A general form of discrete-time stochastic hybrid system with partial information can be formulated as a partially observable discrete-time stochastic hybrid system [5] [9]. However, the complexity of its computation is still a main issue in solving a general PODTSHS.…”

Section: Introductionmentioning

confidence: 99%

“…Ding et al [5] and Lesser [9] extended it to a partially observable framework. We slightly modify the formulation in [5] and [9] and define the partially observable discrete-time stochastic hybrid system as follows:…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we consider a special class in partially observable discrete-time stochastic hybrid system (PODT-SHS) [5] in which only discrete states are hidden and there are only discrete control inputs. There are many applications that can be modeled as such systems, especially for humancentered systems in which the intent of the human operator is unknown and can be modeled as the hidden mode.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An efficient algorithm for discrete-time hidden mode stochastic hybrid systems

Lam

Yang

Sastry

2015

2015 European Control Conference (ECC)

View full text Add to dashboard Cite

Abstract-In this paper, we propose an efficient algorithm to find an optimal control policy in a discrete-time hidden mode stochastic hybrid system, which is a special case of partially observable discrete-time stochastic hybrid systems in which only discrete states are hidden. Many human-centered systems can be modeled as such systems, in which the intent of the human operator is unknown and can be modeled as the hidden mode. In the literature, the optimal control problem of hidden mode stochastic hybrid system is known to have high computational complexity due to the continuous state space. In this paper, we will tackle this computational challenge by using local quadratic functions to approximate the optimal expected reward, which does not have a closed-form expression in general. We will show the efficacy of our proposed method, and the significant improvement in the computational time.

show abstract

The Demon, the Gambler, and the Engineer

Fränzle

Kröger

2018

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Optimal control of partially observable discrete time stochastic hybrid systems for safety specifications

Cited by 18 publications

References 19 publications

Computing probabilistic viable sets for partially observable systems using truncated gaussians and adaptive gridding

Computing probabilistic viable sets for partially observable systems using truncated gaussians and adaptive gridding

An efficient algorithm for discrete-time hidden mode stochastic hybrid systems

The Demon, the Gambler, and the Engineer

Contact Info

Product

Resources

About