Linear Quadratic Regulator

A robust control strategy for autonomous vehicles can improve system stability, enhance riding comfort, and prevent driving accidents. This paper presents a novel interpolation-tubebased constrained iterative linear quadratic regulator (itubeCILQR) algorithm for autonomous computer-vision-based vehicle lane-keeping. The goal of the algorithm is to enhance robustness during high-speed cornering on tight turns. Compared with standard tube-based approaches, the proposed itube-CILQR algorithm reduces system conservatism and exhibits higher computational speed. Numerical simulations and vision-based experiments were conducted to examine the feasibility of using the proposed algorithm for controlling autonomous vehicles. The results indicated that the proposed algorithm achieved superior vehicle lane-keeping performance to variational CILQRbased methods and model predictive control (MPC) approaches involving the use of a classical interior-point optimizer. Specifically, itube-CILQR required an average runtime of 3.45 ms to generate a control signal for guiding a self-driving vehicle. By comparison, itube-MPC typically required a 4.32 times longer computation time to complete the same task. Moreover, the influence of conservatism on system behavior was investigated by exploring the variations in the interpolation variables derived using the proposed itube-CILQR algorithm during lane-keeping maneuvers.

Inspired by REINFORCE, we introduce a novel receding-horizon algorithm for the Linear Quadratic Regulator (LQR) problem with unknown dynamics. Unlike prior methods, our algorithm avoids reliance on two-point gradient estimates while maintaining the same order of sample complexity. Furthermore, it eliminates the restrictive requirement of starting with a stable initial policy, broadening its applicability. Beyond these improvements, we introduce a refined analysis of error propagation through the contraction of the Riccati operator under the Riemannian distance. This refinement leads to a better sample complexity and ensures improved convergence guarantees.

We present a parallel solver for finite-horizon linear-quadratic regulator (LQR) problems with arbitrary stagewise linear equality constraints, using linear work and logarithmic depth in the horizon for fixed local dimensions. The solver uses a two-part reduction that separates feasibility from optimization. First, an associative suffix scan computes the states from which each remaining horizon is feasible. Second, we use these feasible-continuation sets to eliminate the constraints independently at each stage, producing an unconstrained LQR problem with smaller or equal, possibly stage-varying dimensions. A parallel unconstrained-LQR solver completes the primal solution. Finally, we recover valid multipliers from the original KKT stationarity equations using a logarithmic-depth contraction-expansion procedure, even when the multipliers are not unique. Sequential and parallel implementations are validated against dense KKT solutions and original residuals. We release a C++/CUDA implementation with JAX bindings under the MIT license.