15 research outputs found
Dynamic Tube MPC for Nonlinear Systems
Modeling error or external disturbances can severely degrade the performance
of Model Predictive Control (MPC) in real-world scenarios. Robust MPC (RMPC)
addresses this limitation by optimizing over feedback policies but at the
expense of increased computational complexity. Tube MPC is an approximate
solution strategy in which a robust controller, designed offline, keeps the
system in an invariant tube around a desired nominal trajectory, generated
online. Naturally, this decomposition is suboptimal, especially for systems
with changing objectives or operating conditions. In addition, many tube MPC
approaches are unable to capture state-dependent uncertainty due to the
complexity of calculating invariant tubes, resulting in overly-conservative
approximations. This work presents the Dynamic Tube MPC (DTMPC) framework for
nonlinear systems where both the tube geometry and open-loop trajectory are
optimized simultaneously. By using boundary layer sliding control, the tube
geometry can be expressed as a simple relation between control parameters and
uncertainty bound; enabling the tube geometry dynamics to be added to the
nominal MPC optimization with minimal increase in computational complexity. In
addition, DTMPC is able to leverage state-dependent uncertainty to reduce
conservativeness and improve optimization feasibility. DTMPC is demonstrated to
robustly perform obstacle avoidance and modify the tube geometry in response to
obstacle proximity
Collision Probabilities for Continuous-Time Systems Without Sampling [with Appendices]
Demand for high-performance, robust, and safe autonomous systems has grown
substantially in recent years. Fulfillment of these objectives requires
accurate and efficient risk estimation that can be embedded in core
decision-making tasks such as motion planning. On one hand, Monte-Carlo (MC)
and other sampling-based techniques can provide accurate solutions for a wide
variety of motion models but are cumbersome to apply in the context of
continuous optimization. On the other hand, "direct" approximations aim to
compute (or upper-bound) the failure probability as a smooth function of the
decision variables, and thus are widely applicable. However, existing
approaches fundamentally assume discrete-time dynamics and can perform
unpredictably when applied to continuous-time systems operating in the real
world, often manifesting as severe conservatism. State-of-the-art attempts to
address this within a conventional discrete-time framework require additional
Gaussianity approximations that ultimately produce inconsistency of their own.
In this paper we take a fundamentally different approach, deriving a risk
approximation framework directly in continuous time and producing a lightweight
estimate that actually improves as the discretization is refined. Our
approximation is shown to significantly outperform state-of-the-art techniques
in replicating the MC estimate while maintaining the functional and
computational benefits of a direct method. This enables robust, risk-aware,
continuous motion-planning for a broad class of nonlinear, partially-observable
systems.Comment: To appear at RSS 202
Robust Funnel Model Predictive Control for output tracking with prescribed performance
We propose a novel robust Model Predictive Control (MPC) scheme for nonlinear
multi-input multi-output systems of relative degree one with stable internal
dynamics. The proposed algorithm is a combination of funnel MPC, i.e., MPC with
a particular stage cost, and the model-free adaptive funnel controller. The new
robust funnel MPC scheme guarantees output tracking of reference signals within
prescribed performance bounds -- even in the presence of unknown disturbances
and a structural model-plant mismatch. We show initial and recursive
feasibility of the proposed control scheme without imposing terminal conditions
or any requirements on the prediction horizon. Moreover, we allow for model
updates at runtime. To this end, we propose a proper initialization strategy,
which ensures that recursive feasibility is preserved. Finally, we validate the
performance of the proposed robust MPC scheme by simulations