Motivated by stochastic model predictive control applications, we present a semi-algebraic approach to constraint tightening for chance-constrained systems with unbounded additive disturbances and saturated inputs. The saturated error dynamics are handled via their exact piecewise-affine structure, which naturally accommodates asymmetric saturation bounds. A polynomial Lyapunov function satisfying a drift condition is then designed using sum-of-squares optimization, yielding finite-time probabilistic reachable sets and a probabilistic ultimate bound. The set geometry is explicitly optimized for constraint tightening, further reducing conservatism. A numerical example demonstrates the effectiveness of the design.
We study a receding horizon game in which multiple agents drive linear systems subject to additive disturbances, private state and input constraints, and shared coupling constraints. We propose a robust game-theoretic control framework that combines tube-based constraint tighteni…
This paper develops a data-enabled primal-dual framework for learning optimal control policies for unknown linear discrete-time systems from online data. The proposed approach views the data-dependent control synthesis problem as a time-varying semidefinite program (SDP) whose co…
Stochastic resources such as wind farms, electric vehicle aggregators, and demand-side assets are increasingly participating as reserve providers in ancillary service markets. To manage delivery uncertainty, system operators impose minimum reliability thresholds on such providers…
We consider the problem of learning high-dimensional semi-global feedback controllers under hard safety constraints enforced by control barrier functions (CBFs). Incorporating CBFs into end-to-end policy training requires embedding a quadratic-program-based safety filter as an op…
We consider the finite-time optimal control of stochastic systems subject to a probabilistic constraint on the trajectories' safety. Such formulations are known as joint chance constrained optimal control problems. The common practice is to jointly minimise the expected cost of a…
This paper solves the targeting problem focusing on accuracy, computational efficiency, and reliability. The trajectory optimization problem is first recast as a polynomial optimization problem (POP) by leveraging differential algebra to compute high-order Taylor expansions of th…