137,021 research outputs found
Multi-Parametric Extremum Seeking-based Auto-Tuning for Robust Input-Output Linearization Control
We study in this paper the problem of iterative feedback gains tuning for a
class of nonlinear systems. We consider Input-Output linearizable nonlinear
systems with additive uncertainties. We first design a nominal Input-Output
linearization-based controller that ensures global uniform boundedness of the
output tracking error dynamics. Then, we complement the robust controller with
a model-free multi-parametric extremum seeking (MES) control to iteratively
auto-tune the feedback gains. We analyze the stability of the whole controller,
i.e. robust nonlinear controller plus model-free learning algorithm. We use
numerical tests to demonstrate the performance of this method on a mechatronics
example.Comment: To appear at the IEEE CDC 201
Learning an Approximate Model Predictive Controller with Guarantees
A supervised learning framework is proposed to approximate a model predictive
controller (MPC) with reduced computational complexity and guarantees on
stability and constraint satisfaction. The framework can be used for a wide
class of nonlinear systems. Any standard supervised learning technique (e.g.
neural networks) can be employed to approximate the MPC from samples. In order
to obtain closed-loop guarantees for the learned MPC, a robust MPC design is
combined with statistical learning bounds. The MPC design ensures robustness to
inaccurate inputs within given bounds, and Hoeffding's Inequality is used to
validate that the learned MPC satisfies these bounds with high confidence. The
result is a closed-loop statistical guarantee on stability and constraint
satisfaction for the learned MPC. The proposed learning-based MPC framework is
illustrated on a nonlinear benchmark problem, for which we learn a neural
network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter
Learning Stable Koopman Models for Identification and Control of Dynamical Systems
Learning models of dynamical systems from data is a widely-studied problem in control theory and machine learning. One recent approach for modelling nonlinear systems considers the class of Koopman models, which embeds the nonlinear dynamics in a higher-dimensional linear subspace. Learning a Koopman embedding would allow for the analysis and control of nonlinear systems using tools from linear systems theory. Many recent methods have been proposed for data-driven learning of such Koopman embeddings, but most of these methods do not consider the stability of the Koopman model.
Stability is an important and desirable property for models of dynamical systems. Unstable models tend to be non-robust to input perturbations and can produce unbounded outputs, which are both undesirable when the model is used for prediction and control. In addition, recent work has shown that stability guarantees may act as a regularizer for model fitting. As such, a natural direction would be to construct Koopman models with inherent stability guarantees.
Two new classes of Koopman models are proposed that bridge the gap between Koopman-based methods and learning stable nonlinear models. The first model class is guaranteed to be stable, while the second is guaranteed to be stabilizable with an explicit stabilizing controller that renders the model stable in closed-loop. Furthermore, these models are unconstrained in their parameter sets, thereby enabling efficient optimization via gradient-based methods. Theoretical connections between the stability of Koopman models and forms of nonlinear stability such as contraction are established. To demonstrate the effect of the stability guarantees, the stable Koopman model is applied to a system identification problem, while the stabilizable model is applied to an imitation learning problem. Experimental results show empirically that the proposed models achieve better performance over prior methods without stability guarantees
Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear System
This paper proposes a nonlinear policy architecture for control of
partially-observed linear dynamical systems providing built-in closed-loop
stability guarantees. The policy is based on a nonlinear version of the Youla
parameterization, and augments a known stabilizing linear controller with a
nonlinear operator from a recently developed class of dynamic neural network
models called the recurrent equilibrium network (REN). We prove that RENs are
universal approximators of contracting and Lipschitz nonlinear systems, and
subsequently show that the the proposed Youla-REN architecture is a universal
approximator of stabilizing nonlinear controllers. The REN architecture
simplifies learning since unconstrained optimization can be applied, and we
consider both a model-based case where exact gradients are available and
reinforcement learning using random search with zeroth-order oracles. In
simulation examples our method converges faster to better controllers and is
more scalable than existing methods, while guaranteeing stability during
learning transients
Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness
This paper introduces recurrent equilibrium networks (RENs), a new class of
nonlinear dynamical models for applications in machine learning, system
identification and control. The new model class has ``built in'' guarantees of
stability and robustness: all models in the class are contracting - a strong
form of nonlinear stability - and models can satisfy prescribed incremental
integral quadratic constraints (IQC), including Lipschitz bounds and
incremental passivity. RENs are otherwise very flexible: they can represent all
stable linear systems, all previously-known sets of contracting recurrent
neural networks and echo state networks, all deep feedforward neural networks,
and all stable Wiener/Hammerstein models. RENs are parameterized directly by a
vector in R^N, i.e. stability and robustness are ensured without parameter
constraints, which simplifies learning since generic methods for unconstrained
optimization can be used. The performance and robustness of the new model set
is evaluated on benchmark nonlinear system identification problems, and the
paper also presents applications in data-driven nonlinear observer design and
control with stability guarantees.Comment: Journal submission, extended version of conference paper (v1 of this
arxiv preprint
Learning Over All Contracting and Lipschitz Closed-Loops for Partially-Observed Nonlinear Systems
This paper presents a policy parameterization for learning-based control on
nonlinear, partially-observed dynamical systems. The parameterization is based
on a nonlinear version of the Youla parameterization and the recently proposed
Recurrent Equilibrium Network (REN) class of models. We prove that the
resulting Youla-REN parameterization automatically satisfies stability
(contraction) and user-tunable robustness (Lipschitz) conditions on the
closed-loop system. This means it can be used for safe learning-based control
with no additional constraints or projections required to enforce stability or
robustness. We test the new policy class in simulation on two reinforcement
learning tasks: 1) magnetic suspension, and 2) inverting a rotary-arm pendulum.
We find that the Youla-REN performs similarly to existing learning-based and
optimal control methods while also ensuring stability and exhibiting improved
robustness to adversarial disturbances
Optimal control of non-stationary differential linear repetitive processes
Differential repetitive processes are a distinct class of continuousdiscrete 2D linear systems of both systems theoretic and applications interest. The feature which makes them distinct from other classes of such systems is the fact that information propagation in one of the two independent directions only occurs over a finite interval. Applications areas include iterative learning control and iterative solution algorithms for classes of dynamic nonlinear optimal control problems based on the maximum principle, and the modelling of numerous industrial processes such as metal rolling, and long-wall cutting etc. The new results in is paper solve a general optimal problem in the presence of non-stationary dynamics
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