Errors-in-Variables Data-Driven Receding-Horizon LQR

Non-asymptotic Bounds of Learning-based Linear MPC With Input Constraints and Unbounded Stochastic Noise

This paper studies learning-based model predictive control (MPC) for stabilizing unknown discrete-time linear systems with hard input constraints and additive unbounded sub-Gaussian disturbances. We adopt a certainty-equivalence (CE) design that combines a switching MPC control law with online regularized least-squares (RLS) parameter estimation. The resulting switching control law blends the MPC with a saturated deadbeat controller, ensuring global closed-loop stability. Building upon non-asymptotic error bound of least-squares, we derive non-asymptotic, high-probability stability bounds for the closed-loop system under the proposed switching controller. Numerical experiments illustrate and support the theoretical findings.

LQG solution for POMDP without estimating states: A minimum variance approach

This paper investigates the control of discrete-time linear time-invariant (LTI) systems subject to incomplete and corrupted measurements. Specifically, we focus on designing a Linear Quadratic Gaussian (LQG) controller without relying on explicit state estimation. By leveraging minimum variance duality, our approach allows the current control input to be represented as a linear function of available measurements and previously applied inputs, successfully reducing the task to a tractable deterministic optimization problem. We provide theoretical justification for this framework and demonstrate its practical effectiveness through numerical experiments.

On Numerical Solutions of Sampled-Data Control Systems via Differential LMI Optimization

Koopman-based model predictive control for nonlinear systems with bounded model uncertainty

Model predictive control for linear parameter varying systems: a double-sum-free parameter-dependent lyapunov function approach

We present a novel model predictive control framework for linear parameter varying (LPV) systems, leveraging a parameter-dependent Lyapunov function (PDLF) while eliminating the conventional double-sum formulation. Traditional PDLF-based approaches for LPV systems often rely on non-convex double summations, requiring approximation techniques such as sum-of-squares programming to derive tractable linear matrix inequality (LMI) conditions. These approximations introduce increased computational complexity and conservatism, limiting their practical applicability. In this paper, we show that for a class of LPV systems with a constant input matrix, it is possible to derive direct LMI conditions without any approximations by appropriately formulating the PDLF. This approach improves closed-loop performance while ensuring both recursive feasibility and asymptotic stability. Numerical comparisons with earlier solutions from the literature are given to illustrate effectiveness of the proposed method.

Robust Safety Filtering for Input-Constrained Underactuated Linear Systems

We present a robust safety-filtering framework for input-constrained underactuated linear systems subject to unknown disturbances. A baseline H-$\infty$ input is derived from a zero-sum differential game, while a disturbance observer supplies an estimate and a transient error bound. The baseline input is adjusted using the disturbance estimate, while the estimate and its error bound are used to define robust high-order control barrier function constraints; forward invariance holds as long as the admissible-input set remains nonempty. For scalar-input systems, pointwise feasibility is determined from an exact input interval, and the interval width defines the feasibility margin. A finite-horizon H-$\infty$ performance balance accounts for the accumulated deviation of the applied input from the baseline H-$\infty$ policy. Simulations on a linearized two-wheeled balancing robot show how position and body-pitch constraints compete for the same bounded wheel-torque input.