220 research outputs found
Persistently Exciting Tube MPC
This paper presents a new approach to deal with the dual problem of system identification and regulation. The main feature consists of breaking the control input to the system into a regulator part and a persistently exciting part. The former is used to regulate the plant using a robust MPC formulation, in which the latter is treated as a bounded additive disturbance. The identification process is executed by a simple recursive least squares algorithm. In order to guarantee sufficient excitation for the identification, an additional non-convex constraint is enforced over the persistently exciting part
Persistently Exciting Tube MPC
This paper presents a new approach to deal with the dual problem of system identification and regulation. The main feature consists of breaking the control input to the system into a regulator part and a persistently exciting part. The former is used to regulate the plant using a robust MPC formulation, in which the latter is treated as a bounded additive disturbance. The identification process is executed by a simple recursive least squares algorithm. In order to guarantee sufficient excitation for the identification, an additional non-convex constraint is enforced over the persistently exciting part
Stabilizing predictive control with persistence of excitation for constrained linear systems
A new adaptive predictive controller for constrained linear systems is presented. The main feature of the proposed controller is the partition of the input in two components. The first part is used to persistently excite the system, in order to guarantee accurate and convergent parameter estimates in a deterministic framework. An MPC-inspired receding horizon optimization problem is developed to achieve the required excitation in a manner that is optimal for the plant. The remaining control action is employed by a conventional tube MPC controller to regulate the plant in the presence of parametric uncertainty and the excitation generated for estimation purposes. Constraint satisfaction, robust exponential stability, and convergence of the estimates are guaranteed under design conditions mildly more demanding than that of standard MPC implementations
Robust Adaptive Model Predictive Control: Performance and Parameter Estimation
For systems with uncertain linear models, bounded additive disturbances and
state and control constraints, a robust model predictive control algorithm
incorporating online model adaptation is proposed. Sets of model parameters are
identified online and employed in a robust tube MPC strategy with a nominal
cost. The algorithm is shown to be recursively feasible and input-to-state
stable. Computational tractability is ensured by using polytopic sets of fixed
complexity to bound parameter sets and predicted states. Convex conditions for
persistence of excitation are derived and are related to probabilistic rates of
convergence and asymptotic bounds on parameter set estimates. We discuss how to
balance conflicting requirements on control signals for achieving good tracking
performance and parameter set estimate accuracy. Conditions for convergence of
the estimated parameter set are discussed for the case of fixed complexity
parameter set estimates, inexact disturbance bounds and noisy measurements
Data-driven stochastic model predictive control
We propose a novel data-driven stochastic model predictive control (MPC)
algorithm to control linear time-invariant systems with additive stochastic
disturbances in the dynamics. The scheme centers around repeated predictions
and computations of optimal control inputs based on a non-parametric
representation of the space of all possible trajectories, using the fundamental
lemma from behavioral systems theory. This representation is based on a single
measured input-state-disturbance trajectory generated by persistently exciting
inputs and does not require any further identification step. Based on
stochastic MPC ideas, we enforce the satisfaction of state constraints with a
pre-specified probability level, allowing for a systematic trade-off between
control performance and constraint satisfaction. The proposed data-driven
stochastic MPC algorithm enables efficient control where robust methods are too
conservative, which we demonstrate in a simulation example.Comment: This work has been submitted to the L4DC 2022 conferenc
Adaptive robust predictive control with sample-based persistent excitation
We propose a robust adaptive Model Predictive Control (MPC) strategy with
online set-based estimation for constrained linear systems with unknown
parameters and bounded disturbances. A sample-based test applied to predicted
trajectories is used to ensure convergence of parameter estimates by enforcing
a persistence of excitation condition on the closed loop system. The control
law robustly satisfies constraints and has guarantees of feasibility and
input-to-state stability. Convergence of parameter set estimates to the actual
system parameter vector is guaranteed under conditions on reachability and
tightness of disturbance bounds
Adaptive Output Feedback Model Predictive Control
Model predictive control (MPC) for uncertain systems in the presence of hard
constraints on state and input is a non-trivial problem, and the challenge is
increased manyfold in the absence of state measurements. In this paper, we
propose an adaptive output feedback MPC technique, based on a novel combination
of an adaptive observer and robust MPC, for single-input single-output
discrete-time linear time-invariant systems. At each time instant, the adaptive
observer provides estimates of the states and the system parameters that are
then leveraged in the MPC optimization routine while robustly accounting for
the estimation errors. The solution to the optimization problem results in a
homothetic tube where the state estimate trajectory lies. The true state
evolves inside a larger outer tube obtained by augmenting a set, invariant to
the state estimation error, around the homothetic tube sections. The proof for
recursive feasibility for the proposed `homothetic and invariant' two-tube
approach is provided, along with simulation results on an academic system.Comment: 6 page
Model predictive control for linear systems: adaptive, distributed and switching implementations
Thanks to substantial past and recent developments, model predictive control has become one of the most relevant advanced control techniques.
Nevertheless, many challenges associated to the reliance of MPC on a mathematical model that accurately depicts the controlled process still exist.
This thesis is concerned with three of these challenges, placing the focus on constructing mathematically sound MPC controllers that are comparable in complexity to standard MPC implementations.
The first part of this thesis tackles the challenge of model uncertainty in time-varying plants.
A new dual MPC controller is devised to robustly control the system in presence of parametric uncertainty and simultaneously identify more accurate representations of the plant while in operation.
The main feature of the proposed dual controller is the partition of the input, in order to decouple both objectives.
Standard robust MPC concepts are combined with a persistence of excitation approach that guarantees the closed-loop data is informative enough to provide accurate estimates.
Finally, the adequacy of the estimates for updating the MPC's prediction model is discussed.
The second part of this thesis tackles a specific type of time-varying plant usually referred to as switching systems.
A new approach to the computation of dwell-times that guarantee admissible and stable switching between mode-specific MPC controllers is proposed.
The approach is computationally tractable, even for large scale systems, and relies on the well-known exponential stability result available for standard MPC controllers.
The last part of this thesis tackles the challenge of MPC for large-scale networks composed by several subsystems that experience dynamical coupling.
In particular, the approach devised in this thesis is non-cooperative, and does not rely on arbitrarily chosen parameters, or centralized initializations.
The result is a distributed control algorithm that requires one step of communication between neighbouring subsystems at each sampling time, in order to properly account for the interaction, and provide admissible and stabilizing control
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