Gerardo De La Torre

Improving transient performance of adaptive control architectures using frequency-limited system error dynamics

Although adaptive control theory offers mathematical tools to achieve system performance without excessive reliance on dynamical system models, its applications to safety-critical systems can be limited due to poor transient performance and robustness. In this paper, we develop an adaptive control architecture to achieve stabilisation and command following of uncertain dynamical systems with improved transient performance. Our framework consists of a new reference system and an adaptive controller. The proposed reference system captures a desired closed-loop dynamical system behaviour modified by a mismatch term representing the high-frequency content between the uncertain dynamical system and this reference system, i.e., the system error. In particular, this mismatch term allows the frequency content of the system error dynamics to be limited, which is used to drive the adaptive controller. It is shown that this key feature of our framework yields fast adaptation without incurring high-frequency oscillations in the transient performance. We further show the effects of design parameters on the system performance, analyse closeness of the uncertain dynamical system to the unmodified (ideal) reference system, discuss robustness of the proposed approach with respect to time-varying uncertainties and disturbances, and make connections to gradient minimisation and classical control theory. A numerical example is provided to demonstrate the efficacy of the proposed architecture.

Frequency-limited adaptive control architecture for transient response improvement

This paper presents a new adaptive control architecture to achieve stabilization and command following of uncertain dynamical systems with improved transient performance. Our framework consists of a new reference system and an adaptive controller. The proposed reference system captures a desired closed-loop dynamical system behavior modified by a mismatch term representing the high-frequency content between the uncertain dynamical system and this reference system, i.e., the system error. In particular, this mismatch term allows one to limit the frequency content of the system error dynamics, which is used to drive the adaptive controller. It is shown that this key feature of our framework yields fast adaptation without incurring high-frequency oscillations in the transient performance.

Autonomous suspended load operations via trajectory optimization and variational integrators

This paper presents a real-time implementable trajectory optimization framework for autonomous suspended load operations in outdoor environments. The framework solves the posed optimal control problem with the iteration-based differential dynamic programming algorithm. The algorithm uses a variational integrator to propagate the modeled system’s state configuration and linearize the resulting discrete dynamics. The variational integrator is an excellent candidate for real-time implementation because it remains accurate despite relatively large discretization time steps. Therefore, the computational effort of the differential dynamic programming algorithm can be mitigated through the reduction of discrete time points. The state of the slung load is estimated via an augmentation to the existing navigation system that only uses vision-based measurements of the load. Simulation studies and a flight test are presented to demonstrate the effectiveness of the proposed framework.

Resilient networked multiagent systems: A distributed adaptive control approachy

Control algorithms of networked multiagent systems are generally computed distributively without having a centralized entity monitoring the activity of agents; and therefore, adverse events such as attacks to the communication network and/or failure of agent-wise components can easily result in system instability and prohibit the accomplishment of system-level objectives. This paper studies resilient coordination of networked multiagent systems in the presence of misbehaving agents, i.e., agents that are subject to such adverse events. In particular, we consider a class of adverse conditions consisting of exogenous disturbances and interagent uncertainties, and present a distributed adaptive control architecture to retrieve the nominal networked multiagent system behavior. Departing from the existing relevant literature that make specific assumptions on the graph topology and/or the fraction of misbehaving agents, we show that the considered class of adverse conditions can be mitigated through a new adaptive control methodology that utilizes a local state emulator - even if all agents are misbehaving. A illustrative numerical example is provided to demonstrate the theoretical findings.

Application of Frequency-Limited Adaptive Quadrocopter Control

Adaptive control systems have long been used to effectively control dynamical systems without excessive reliance on system models. This is due mainly to the fact that adaptive control guarantees stability, the same however, cannot be said for performance; adaptive control systems may exhibit poor tracking during transient (learning) time. This paper discusses the experimental implementation of a new architecture to model reference adaptive control, specifically, the reference system is augmented with a novel mismatch term representing the high-frequency content of the system tracking error. This mismatch term is an effective tool to remove the high frequency content of the error signal used in the adaptive element update law. The augmented architecture therefore allows high-gain adaptation without the usual side-effect of high-frequency oscillations. The proposed control architecture is validated using the Georgia Tech unmanned aerial vehicle simulation tool (GUST) and also implemented on the Georgia Tech Quadrocpoter (GTQ). It is shown that the new framework allows the system to quickly suppress the effect of uncertainty without the usual side effects of high gain adaptation such as high-frequency oscillations.

Adaptive Spacecraft Control: Stability, Performance, and Robustness

This paper designs a low-frequency learning adaptive control architecture for a flexible spacecraft. The proposed architecture involves a new and novel controller structure involving a modification term in the update law. In particular, this modification term filters out the high-frequency content contained in the update law while preserving stability of the system error dynamics. This key feature of our design allows for robust, fast adaptation in the face of high-gain learning rates. A numerical illustrative study is provided for a flexible spacecraft to demonstrate the efficacy of the proposed design.

Adaptive architectures for resilient control of networked multiagent systems in the presence of misbehaving agents

ABSTRACT Control algorithms of networked multiagent systems are generally computed distributively without having a centralised entity monitoring the activity of agents; and therefore, unforeseen adverse conditions such as uncertainties or attacks to the communication network and/or failure of agent-wise components can easily result in system instability and prohibit the accomplishment of system-level objectives. In this paper, we study resilient coordination of networked multiagent systems in the presence of misbehaving agents, i.e. agents that are subject to exogenous disturbances that represent a class of adverse conditions. In particular, a distributed adaptive control architecture is presented for directed and time-varying graph topologies to retrieve a desired networked multiagent system behaviour. Apart from the existing relevant literature that make specific assumptions on the graph topology and/or the fraction of misbehaving agents, we show that the considered class of adverse conditions can be mitigated by the proposed adaptive control approach that utilises a local state emulator – even if all agents are misbehaving. Illustrative numerical examples are provided to demonstrate the theoretical findings.

Model-Based Control Using Koopman Operators

This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting model-based control. Specifically, we illustrate how the operator can be used to obtain a linearizable data-driven model for an unknown dynamical process that is useful for model-based control synthesis. Simulated results show that with increasing complexity in the choice of the basis functions, a closed-loop controller is able to invert and stabilize a cart- and VTOL-pendulum systems. Furthermore, the specification of the basis function are shown to be of importance when generating a Koopman operator for specific robotic systems. Experimental results with the Sphero SPRK robot explore the utility of the Koopman operator in a reduced state representation setting where increased complexity in the basis function improve open- and closed-loop controller performance in various terrains, including sand.

Reference control architecture in the presence of measurement noise and actuator dynamics

In this paper the command governor-based model reference control architecture is developed and analyzed for uncertain dynamical systems in the presence measurement noise and actuator dynamics. Specifically, the command governor is a dynamical system that adjusts the trajectory of a given command in order to enable an uncertain system to be able to follow an ideal reference system capturing a desired closed-loop dynamical system behavior both in transient-time and steady-state. In this paper, we present modifications to the original command governor approach in order to increase its robustness properties against measurement noise and actuator dynamics. In particular, the modified architecture is shown to retain closed-loop system stability and predictable transient and steady-state performance. Illustrative numerical results are found to verify the theoretical findings.

Bounded Hybrid Connectivity Control of Networked Multiagent Systems

Connectivity refers to the problem that the initial information flow between a group of agents is required to be preserved for all time in order to achieve a given set of system-level objectives. This technical note focuses on a new connectivity control architecture for networked multiagent systems based on hybrid protocols. Specifically, for a group of agents subject to Δ-disk proximity graphs, we consider the consensus problem while preserving connectedness with a priori given bounds on the control inputs. The bounds on the control inputs are shown neither to depend on potential functions nor system states. Instead the bounds are user selected continuous functions. Using the proposed framework, we show that the maximum distance among neighboring agents strictly decreases, and hence, the connectivity problem is solved while satisfying the consensus objective. Illustrative numerical examples are provided to demonstrate the efficacy of the proposed bounded hybrid connectivity control architecture.