Backstepping for nonlinear PDEs yields exact feedback linearizing laws in the form of infinite Volterra series -- elegant in theory, but with challenges for implementation. This paper shows that even very low-order truncations of such controllers, no longer exactly linearizing, retain the stabilizing power. The key insight is that higher-order terms become negligible near the origin, so stability is recovered for any fixed truncation order by restricting the initial condition size. We establish spatial sup-norm results: finite-time practical stability and asymptotic stability characterized by a class-$\mathcal{KL}$ estimate. The region-of-attraction estimate grows with the truncation order and shrinks with the growth rate of the nonlinearity. The analysis overcomes the lack of pointwise kernel bounds and resolves well-posedness of the nonlinear closed loop, showing that surprisingly simple approximations already capture the essence of nonlinear PDE feedback linearization.
Volterra series feedback linearizes a class of nonlinear hyperbolic PDEs but produces a controller that, even after truncation, demands solving a tower of plant-specific kernel PDEs and evaluating nested integrals. We prove the truncated controller is jointly Lipschitz in plant a…
Adaptive control learns the plant online; neural-operator control learns the control gains offline. We bring the two together for a class of nonlinear hyperbolic PDEs whose dynamics are governed by an unknown Volterra series of arbitrarily many kernels. An observer-based passive…
Input--output feedback linearization fails at decoupling singularities, where the decoupling matrix loses rank, the relative degree is lost, and the linearizing control becomes unbounded. This paper develops a singularity-robust trajectory-tracking controller for square nonlinear…
This paper studies real-time robust optimal control for uncertain nonlinear systems, where linear time-varying (LTV) approximations make planning tractable but require sound linearization error bounds (LEBs) to guarantee robust constraint satisfaction. We develop tight, different…
Physical sensing and actuation noise floors should inform how much belief resolution a decision-making system can reliably use. We introduce Finite Reliability Representations (FRR), a framework for covering belief spaces by reliability cells: regions within which the optimal act…
We establish finite-sample closed-loop stability guarantees for Model Predictive Path Integral (MPPI) control applied to discrete-time Linear Time-Invariant (LTI) systems with additive Gaussian process disturbances. The key observation is that, for unconstrained LTI/quadratic sys…