33 research outputs found
Learning Robustness with Bounded Failure: An Iterative MPC Approach
We propose an approach to design a Model Predictive Controller (MPC) for
constrained Linear Time Invariant systems performing an iterative task. The
system is subject to an additive disturbance, and the goal is to learn to
satisfy state and input constraints robustly. Using disturbance measurements
after each iteration, we construct Confidence Support sets, which contain the
true support of the disturbance distribution with a given probability. As more
data is collected, the Confidence Supports converge to the true support of the
disturbance. This enables design of an MPC controller that avoids conservative
estimate of the disturbance support, while simultaneously bounding the
probability of constraint violation. The efficacy of the proposed approach is
then demonstrated with a detailed numerical example.Comment: Added GitHub link to all source code
Multi-Rate Control Design Leveraging Control Barrier Functions and Model Predictive Control Policies
In this paper we present a multi-rate control architecture for safety
critical systems. We consider a high level planner and a low level controller
which operate at different frequencies. This multi-rate behavior is described
by a piecewise nonlinear model which evolves on a continuous and a discrete
level. First, we present sufficient conditions which guarantee recursive
constraint satisfaction for the closed-loop system. Afterwards, we propose a
control design methodology which leverages Control Barrier Functions (CBFs) for
low level control and Model Predictive Control (MPC) policies for high level
planning. The control barrier function is designed using the full nonlinear
dynamical model and the MPC is based on a simplified planning model. When the
nonlinear system is control affine and the high level planning model is linear,
the control actions are computed by solving convex optimization problems at
each level of the hierarchy. Finally, we show the effectiveness of the proposed
strategy on a simulation example, where the low level control action is updated
at a higher frequency than the high level command
Multi-Rate Control Design Leveraging Control Barrier Functions and Model Predictive Control Policies
In this letter we present a multi-rate control architecture for safety critical systems. We consider a high level planner and a low level controller which operate at different frequencies. This multi-rate behavior is described by a piecewise nonlinear model which evolves on a continuous and a discrete level. First, we present sufficient conditions which guarantee recursive constraint satisfaction for the closed-loop system. Afterwards, we propose a control design methodology which leverages Control Barrier Functions (CBFs) for low level control and Model Predictive Control (MPC) policies for high level planning. The control barrier function is designed using the full nonlinear dynamical model and the MPC is based on a simplified planning model. When the nonlinear system is control affine and the high level planning model is linear, the control actions are computed by solving convex optimization problems at each level of the hierarchy. Finally, we show the effectiveness of the proposed strategy on a simulation example, where the low level control action is updated at a higher frequency than the high level command
Learning to Satisfy Unknown Constraints in Iterative MPC
We propose a control design method for linear time-invariant systems that
iteratively learns to satisfy unknown polyhedral state constraints. At each
iteration of a repetitive task, the method constructs an estimate of the
unknown environment constraints using collected closed-loop trajectory data.
This estimated constraint set is improved iteratively upon collection of
additional data. An MPC controller is then designed to robustly satisfy the
estimated constraint set. This paper presents the details of the proposed
approach, and provides robust and probabilistic guarantees of constraint
satisfaction as a function of the number of executed task iterations. We
demonstrate the safety of the proposed framework and explore the safety vs.
performance trade-off in a detailed numerical example.Comment: Long version of the final paper for IEEE-CDC 2020. First two authors
contributed equall