In this paper, we present an equivalent convex optimization formulation for discrete-time stochastic linear systems subject to linear chance constraints, alongside a tight convex relaxation for quadratic chance constraints. By lifting the state vector to encode moment information explicitly, the formulation captures linear chance constraints on states and controls across multiple time steps exactly, without conservatism, yielding strict improvements in both feasibility and optimality. For quadratic chance constraints, we derive convex approximations that are provably less conservative than existing methods. We validate the framework on minimum-snap trajectory generation for a quadrotor, demonstrating that the proposed approach remains feasible at noise levels an order of magnitude beyond the operating range of prior formulations.
Figures & tables
Fig. 1 : Minimum Snap Path Planning for the linearized lateral dynamics of a quadrotor under the two different setups under stochastic perturbation forces ( σ1=σ2=0.05 ). The proposed approach leads to a cost reduction as compared to [ 7 ] , as it can shape the covariance.
TABLE II : Performance comparison across varying noise levels ( σ ) and environment parameters for the Circle Arena and Funnel Corridor scenarios. ✓ and × indicate successful completion and infeasibility, respectively.
This paper proposes a strictly convex chance-constrained stochastic control framework that accounts for uncertainty in control specifications such as reference trajectories and operational constraints. Control inputs and risk allocation are jointly optimized under general, possibly non-Gaussian, uncertainties through sufficient deterministic conditions for probabilistic constraint satisfaction. A decreasing risk regularizer ensures existence and full use of the allowable risk. Under the stated regularity assumptions, the joint solution is unique and locally Lipschitz-continuous, supporting stable numerical optimization. The formulation is extended to learning-based exactly linearizable (EL) models through monotone state and input transformations. A hybrid powertrain example compares deterministic control, equal risk allocation, and optimized risk allocation with and without regularization in terms of charge sustaining, constraint violations, closed-loop cost, and solver time.
Teruki Kato, Ryotaro Shima, Kenji Kashima
Toyota Central R&D Labs., Inc., Nagakute, Aichi, Japan · Graduate School of Informatics, Kyoto University, Kyoto, Japan
This paper presents novel method for distribution-free robust trajectory optimization and control of discrete-time, nonlinear, and non-Gaussian stochastic systems, with closed-loop guarantees on chance constraint satisfaction. Our framework employs conformal inference to generate coverage-based confidence sets for the closed-loop dynamics around arbitrary reference trajectories, by constructing a joint nonconformity score to quantify both the validity of contraction (i.e., incremental stability) conditions and the impact of external stochastic disturbance on the closed-loop dynamics, without any distributional assumptions. Via appropriate constraint tightening, chance constraints can be reformulated into tractable, statistically valid deterministic constraints on the reference trajectories. This enables a formal pathway to leverage and validate learning-based motion planners and controllers, such as those with neural contraction metrics, in safety-critical real-world applications. Notably, our statistical guarantees are non-diverging and can be computed with finite samples of the underlying uncertainty, without overly conservative structural priors. We demonstrate our approach in motion planning problems for designing safe, dynamically feasible trajectories in both numerical simulation and hardware experiments.
Rihan Aaron D'Silva, Hiroyasu Tsukamoto
Department of Aerospace Engineering, The Grainger College of Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois 61801
In this paper, we consider stochastic optimal control problems with infinite-horizon joint chance constraints. By means of an appropriate state augmentation, we reformulate the original problem as a constrained Markov decision process, in which both the cost and the constraint function exhibit an additive structure. We then prove that this formulation enjoys strong duality, thereby enabling us to reformulate the problem as an equivalent unconstrained one in the Lagrange dual framework. We propose a dual-ascent algorithm to solve the resulting problem and show that it converges to a deterministic Markov policy defined over the augmented state space that is both optimal and feasible. To accommodate continuous state-input spaces, we propose a dedicated learning algorithm to approximate the value function in an offline training setting, thereby significantly reducing the computational complexity of the online control phase. We then test our approach on a numerical example and demonstrate its effectiveness compared to online predictive control methods in terms of performance and computational complexity.
Francesco Cordiano, Kanghui He, Bart De Schutter
Delft Center for Systems and Control, Delft University of Technology, 2628 CD, Delft, The Netherlands · Department of Engineering Science, University of Oxford, OX1 3PJ Oxford, U.K.