The Internal Model Principle for Systems with Unbounded Control and Observation

In this paper the theory of robust output regulation of distributed parameter systems with infinite-dimensional exosystems is extended for plants with unbounded control and observation. As the main result, we present the internal model principle for linear infinite-dimensional systems with unbounded input and output operators. We do this for two different definitions of an internal model found in the literature, namely, the p-copy internal model and the $\mathcal{G}$-conditions. We also introduce a new way of defining an internal model for infinite-dimensional systems. The theoretic results are illustrated with an example where we consider robust output tracking for a one-dimensional heat equation with boundary control and pointwise measurements.Comment: 38 pages, 2 figures, in revie

Optimal Output Regulation for Square, Over-Actuated and Under-Actuated Linear Systems

This paper considers two different problems in trajectory tracking control for linear systems. First, if the control is not unique which is most input energy efficient. Second, if exact tracking is infeasible which control performs most accurately. These are typical challenges for over-actuated systems and for under-actuated systems, respectively. We formulate both goals as optimal output regulation problems. Then we contribute two new sets of regulator equations to output regulation theory that provide the desired solutions. A thorough study indicates solvability and uniqueness under weak assumptions. E.g., we can always determine the solution of the classical regulator equations that is most input energy efficient. This is of great value if there are infinitely many solutions. We derive our results by a linear quadratic tracking approach and establish a useful link to output regulation theory.Comment: 8 pages, 0 figures, final version to appear in IEEE Transactions on Automatic Contro

Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

Output tracking via sliding modes in causal systems with time delay modeled by higher order pade approximations

Output tracking in a SISO causal uncertain nonlinear system with an output subject to a time delay is considered using sliding mode control. A higher order Pade approximation to a delay function with a known time delay is used to construct a model of a transformed system without a time delayed output and is employed in a feedback sliding mode control. This model functions as a predictor of the plant states and the plant output, but is of nonminimum phase due to the application of the Pade approximation. The method of the stable system center is used to stabilize the internal dynamics of this plant model, and a control is developed using a sliding surface to allow the plant to track an arbitrary reference profile given by an exogenous system with a known characteristic equation. Simulations of the system are performed for the plant model using a first, second and third order Pade approximations and a controller in plant feedback mode. Numerical examples for Pade approximations of increasing order are considered and compare

Knowledge Transfer Between Robots with Similar Dynamics for High-Accuracy Impromptu Trajectory Tracking

In this paper, we propose an online learning approach that enables the inverse dynamics model learned for a source robot to be transferred to a target robot (e.g., from one quadrotor to another quadrotor with different mass or aerodynamic properties). The goal is to leverage knowledge from the source robot such that the target robot achieves high-accuracy trajectory tracking on arbitrary trajectories from the first attempt with minimal data recollection and training. Most existing approaches for multi-robot knowledge transfer are based on post-analysis of datasets collected from both robots. In this work, we study the feasibility of impromptu transfer of models across robots by learning an error prediction module online. In particular, we analytically derive the form of the mapping to be learned by the online module for exact tracking, propose an approach for characterizing similarity between robots, and use these results to analyze the stability of the overall system. The proposed approach is illustrated in simulation and verified experimentally on two different quadrotors performing impromptu trajectory tracking tasks, where the quadrotors are required to accurately track arbitrary hand-drawn trajectories from the first attempt.Comment: European Control Conference (ECC) 201