Chance-constrained Optimal Control Research Articles

A statistical moment-based spectral approach to the chance-constrained stochastic optimal control of epidemic models

This paper presents a spectral approach to the uncertainty management in epidemic models through the formulation of chance-constrained stochastic optimal control problems. Specifically, a statistical moment-based polynomial expansion is used to calculate surrogate models of the stochastic state variables of the problem that allow for the efficient computation of their main statistics as well as their marginal and joint probability density functions at each time instant, which enable the uncertainty management in the epidemic model. Moreover, the surrogate models are employed to perform the corresponding sensitivity and risk analyses. The proposed methodology provides the designers of the optimal control policies with the capability to increase the predictability of the outcomes by adding suitable chance constraints to the epidemic model and formulating a proper cost functional. The chance-constrained optimal control of a COVID-19 epidemic model is considered in order to illustrate the practical application of the proposed methodology.

Chance-constrained sneaking trajectory planning for reconnaissance robots

Mobile robots have been widely used in various military applications, where an efficient and robust trajectory planner is of vital importance. In this paper, we focus on the sneaking trajectory planning of reconnaissance robots with consideration of uncertainty in the geometric parameters of the watchtower's searchlight. By analyzing the motion equations and the mission requirements, the trajectory planning problem is formulated as a chance-constrained optimal control problem. The convex bounding method, as a kind of sampling technique, is one of the most effective ways to address this optimization problem. However, it suffers from low computational efficiency since a great number of samples are required to chance constraints into determined ones. Calculating the constraint violation rate by numerical integration instead of sampling, a numerical integration assisted convex bounding method is developed. The improved method outperforms computational efficiency since the times of evaluating each constraint becomes less. The developed method is validated by two scenarios with different complexities. Numerical results demonstrate that, compared with the traditional method, the improved method can achieve satisfactory constraint violation rate of similar level but with higher computational efficiency. An animation of the simulation results is available at www.bilibili.com/video/BV1Bg41117xi/.

Risk-Aware Path Planning for Unmanned Aerial Systems in a Spreading Wildfire

Path planning for small unmanned aerial systems (SUAS) in the presence of poorly understood and dynamic obstacles is a challenging problem: for example, flight over a spreading wildfire. Evidential information fusion is used to estimate the current wildfire state and the resulting heat aura at flight level. This approach accounts for ignorance, which is a result of conflict among sensors operating in a harsh environment and a computational forecasting agent that uses a fire evolution model of inadequate accuracy. An SUAS is employed to visit locations of high conflict to provide additional situational awareness. Flight-level heat aura is modeled as a keepout zone with probabilistic boundaries for SUAS path planning. A novel unsupervised classification algorithm is developed to identify distinct obstacle boundaries within the estimated heat aura. Path planning is posed as a chance-constrained optimal control problem, which is transcribed to a nonlinear program via pseudospectral discretization. The results show that this approach can yield a family of solutions that elicit the risk associated with each mission design, and the appropriate choice of risk can aid in the generation of “keyhole paths.”

UAV trajectory optimization using chance-constrained second-order cone programming

It is challenging to generate optimal trajectories for nonlinear dynamic systems under external disturbances. In this brief, we present a novel approach for planning safe trajectories of the chance-constrained trajectory optimization problems with nonconvex constraints. First, the chance constraints are handled by deterministic ones which show its availability. We derive an iterative convex optimization method to solve the optimal control problem. Then the chance-constrained optimal control (CCOCP) problem is reformed to be a nonlinear programming problem (NLP) through the hp-adaptive pseudospectral method. An iterative successive linearization algorithm is detailed to convex the NLP to be a convex optimization one which described as a second-order cone programming problem. We demonstrate the proposed approach on a 3-DoF of unmanned aerial vehicle system under chance-constrained. The simulation results show reliable solutions for the UAV chance-constrained trajectory optimization problem.

Chance-constrained path planning in narrow spaces for a dubins vehicle

The problem of optimal path planning through narrow spaces in an unstructured environment is considered. The optimal path planning problem for a Dubins agent is formulated as a chance-constrained optimal control problem (CCOCP), wherein the uncertainty in obstacle boundaries is modelled using standard probability distributions. The chance constraints are transformed to deterministic equivalents using the inverse cumulative distribution function and subsequently incorporated into a deterministic optimal control problem. Due to multiple convex sub-regions introduced by the obstacles, the initial guess provided to optimal control solver is crucial for computation time and optimality of the solution. A constrained Delaunay triangulation mesh based approach is developed that ensures the initial guess to lie in the optimal sub-convex region. Finally, off-the-shelf software is used to transcribe the optimal control problem to a nonlinear program (NLP) using Gaussian quadrature orthogonal collocation and solved to obtain an optimal path that conforms to system dynamics. By varying the upper bound on probability of obstacle collision, a family of solutions is generated, parameterized by the risk associated with each solution. This approach enables discovery of special “keyhole trajectories” that can provide significant cost savings in a tightly-spaced obstacle field. Merits of this approach are illustrated by comparing it with the traditional bounded uncertainty approach.

Stochastic Model Predictive Control Based Reference Planning for Automated Open-Water Channels

A stochastic model predictive control scheme is developed within the context of planning water-level references for an automated channel. The references are provided as inputs to decentralized feedback controllers that regulate the capacity for gravity-fed supply of flow at points along the channel. An operational challenge is to comply with constraints on channel-flow and water-level transients in the automatic response to changes in the off-take flow load and water-level references. The proposed approach is to determine the reference inputs using a model of the channel dynamics that includes a forecast of off-take demand. Specifically, a structured probabilistic representation of the forecast is used to formualte a chance-constrained optimal control problem that is solved in a receding horizon fashion. A scenario-based approximation of this difficult optimal control problem is considered. The size of the approximating quadratic program scales with the prediction horizon and the number of water-level regulation points. But importantly, the size does not ultimately depend on the number of scenarios used to construct the approximation. Simulations and experimental results from an operational channel are presented to demonstrate the method.

Trajectory planning for hypersonic reentry vehicle satisfying deterministic and probabilistic constraints

The present work explores the optimal flight of aero-assisted reentry vehicles during the atmospheric entry flight phase with the consideration of both deterministic and control chance constraints. To describe the mission profile, a chance-constrained optimal control model is established. Due to the existence of probabilistic constraints (chance constraints), standard numerical trajectory planning algorithms cannot be directly applied to address the considered problem. Hence, we firstly present an approximation-based strategy to replace the probabilistic constraint by a deterministic version. In this way, the transformed optimal control model becomes solvable for standard trajectory optimization methods. In order to obtain enhanced computational performance, an alternative convex-relaxed optimal control formulation is also given. This is achieved by convexifying the vehicle nonlinear dynamics/constraints and by introducing a convex probabilistic constraint handling strategy. Numerical simulations are provided to demonstrate the effectiveness of these two chance-constrained optimization approaches and the corresponding probabilistic constraint handling strategies.

Chance-Constraint-Based Design of Open-Loop Controllers for Linear Uncertain Systems

This paper considers the problem of state-to-state transition with state and control constraints, for a linear system with time-invariant model parameter uncertainties. Polynomial chaos is used to transform the stochastic model to a deterministic surrogate model. This surrogate model is used to pose a chance-constrained optimal control problem where the state constraints and the residual energy cost are represented in terms of the mean and variance of the stochastic states. The resulting convex optimization problem is numerically illustrated on the problem of rest-to-rest maneuver of the benchmark floating oscillator and on an experimental two-tank setup.

Split-Bernstein Approach to Chance-Constrained Optimal Control

In this paper, a semianalytical parametric approximation of chance constraints, called the split-Bernstein approximation, is employed to construct a framework for posing and solving chance-constrained optimal control problems. Dynamic systems with deterministic as well as stochastically perturbed dynamics are considered. In both cases, the chance-constrained optimal control problem is converted into a chance-constrained program, which is transcribed to a nonlinear program using the split-Bernstein approximation. Discretization of deterministic optimal control problems is performed via pseudospectral collocation. For systems perturbed by white noise, a shooting method is used that imposes dynamic constraints implicitly via ensemble propagation. The split-Bernstein approximation of chance constraints allows the solution of the resulting nonlinear program using off-the-shelf gradient-based nonlinear program solvers.

Chance-constrained optimal control for multireservoir system optimization and risk analysis

A vast array of techniques have been developed and applied to optimal operation of large-scale multireservoir systems. Researchers continue to be challenged by the highly complex, stochastic, nonlinear, and high dimensional nature of this dynamic optimization problem. An optimal control model is presented which incorporates chance-constraints on system state variables that assure satisfaction of operational restrictions under specified levels of reliability. The chance-constrained optimal control (CCOC) model is tested on a four-reservoir case study, and its performance assessed based on various quantitative and qualitative criteria, including maintenance of acceptable levels of risk and provision of risk-benefit trade-off information. The concepts of reliability, resiliency and vulnerability are utilized to characterize operating policies generated by the algorithm. CCOC is recommended for operational guidance of large-scale multireservoir systems due to its robustness, flexibility, modest computational requirements, and ability to include risk considerations directly impacting the choice of operational schemes.