Measuring Target Predictability for Optimal Environment Design

Ornik, Melkior

doi:10.1109/cdc42340.2020.9304082

Cited by 4 publications

(3 citation statements)

References 12 publications

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“…For instance, [6], [7], [9] consider predictability as system's sensitivity to initial error and have found great applications in meteorology. [12]- [15] either directly use entropy or define entropy-based quantities to measure the predictability of various Markov decision processes (MDP), and then use these entropy-based indexes to give performance analysis on specific prediction tasks. These analyses view the prediction performance from the perspective of information theory rather than from traditional methods, such as root-mean-square-error, patter correlation (PC) and probability, etc.…”

Section: A Related Workmentioning

confidence: 99%

Predictability of Stochastic Dynamical Systems: Metric, Optimality and Application

Xu¹,

He²,

Li³

2022

Preprint

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Predicting the trajectory of stochastic dynamical systems (SDSs) is an intriguing problem in numerous fields, where characterizing the predictability of SDSs is of fundamental importance. Prior works have tackled this issue by indirectly investigating the uncertainty of distribution in each prediction. How accurately the trajectory of SDSs can be directly predicted still remains open. This paper proposes a new metric, namely predictability exponent, to characterize the decaying rate of probability that the prediction error never exceeds arbitrary . To evaluate predictability exponent, we begin with providing a complete framework for model-known cases. Then, we bring to light the explicit relationship between predictability exponent and entropy by discrete approximation techniques. The definition and evaluation on predictability exponent are further extended to model-unknown cases by optimizing over model spaces, which build a bridge between the accuracy of trajectory predictions and popular entropy-based uncertainty measures. Examples of unpredictable trajectory design are presented to elaborate the applicability of the proposed predictability metric. Simulations are conducted to illustrate the efficiency of the obtained results.

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Section: A Related Workmentioning

confidence: 99%

Predictability of Stochastic Dynamical Systems: Metric, Optimality and Application

Xu¹,

He²,

Li³

2022

Preprint

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“…Algorithm 1: Optimal Control Algorithm with State Unpredictable Input: The initial and target states of the system, x 0 , x o N ; The parameters of the system dynamic, A k , B k ; The parameters of the optimization object, H, Q k , R k , λ 1 , λ 2 , λ 3,k ; The control duration and time steps, T, N ; The upper bound of |u k |, u; Output: The optimal control policy, u 0:N −1 ; Calculate J 1,N , J 2,N and set J 3,N = 0; if without input constraints, u = ∞ then for i = N − 1 to 0 do Calculate P i , G i , M i with ( 12); Calculate W i , Z i and J 1,i , J 2,i , J Calculate µ j and σ j with (11) or (20); Generate a stochastic perturbation δ j from the uniform distribution as ( 16); Obtain the control input u j = µ j + δ j ; Calculate the next state x j+1 with (1); end return The control sequence u 0:N −1 .…”

Section: Dealing With Simple Input-constraintsmentioning

confidence: 99%

“…For instance, [9] uses extended Kalman filter to estimate the states of a moving object and predict its trajectory by a UAV and [10] presents a multiple model unscented Kalman filter to predict multi-agent trajectory. [11] studies the problem that how to detect an agent's objective…”

Section: Introductionmentioning

confidence: 99%

Multi-period Optimal Control for Mobile Agents Considering State Unpredictability

Chendi¹,

He²,

Li³

2022

Preprint

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The optimal control for mobile agents is an important and challenging research issue. Recent work shows that using randomized mechanism in agents' control can make the state unpredictable, and thus ensure the security of agents. However, the unpredictable design is only considered in single period, which can lead to intolerable control performance in long time horizon. This paper aims at the trade-off between the control performance and state unpredictability of mobile agents in long time horizon. Utilizing random perturbations consistent with uniform distributions to maximize the attackers' prediction errors of future states, we formulate the problem as a multi-period convex stochastic optimization problem and solve it through dynamic programming. Specifically, we design the optimal control strategy considering both unconstrained and input constrained systems. The analytical iterative expressions of the control are further provided. Simulation illustrates that the algorithm increases the prediction errors under Kalman filter while achieving the control performance requirements successfully.

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Predictability of Stochastic Dynamical System: A Probabilistic Perspective

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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Measuring Target Predictability for Optimal Environment Design

Cited by 4 publications

References 12 publications

Predictability of Stochastic Dynamical Systems: Metric, Optimality and Application

Predictability of Stochastic Dynamical Systems: Metric, Optimality and Application

Multi-period Optimal Control for Mobile Agents Considering State Unpredictability

Predictability of Stochastic Dynamical System: A Probabilistic Perspective

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