John F. Quindlen

Case Studies in Data-Driven Verification of Dynamical Systems

We interpret several dynamical system verification questions, e.g., region of attraction and reachability analyses, as data classification problems. We discuss some of the tradeoffs between conventional optimization-based certificate constructions with certainty in the outcomes and this new date-driven approach with quantified confidence in the outcomes. The new methodology is aligned with emerging computing paradigms and has the potential to extend systematic verification to systems that do not necessarily admit closed-form models from certain specialized families. We demonstrate its effectiveness on a collection of both conventional and unconventional case studies including model reference adaptive control systems, nonlinear aircraft models, and reinforcement learning problems.

Hybrid model reference adaptive control for unmatched uncertainties

This paper presents a hybrid model reference adaptive control approach for systems with both matched and unmatched uncertainties. This approach extends concurrent learning adaptive control to a wider class of systems with unmatched uncertainties that lie outside the space spanned by the control input, and therefore cannot be directly suppressed with inputs. The hybrid controller breaks the problem into two parts. First, a concurrent learning identification law guarantees the estimates of the unmatched parameterization converges to the actual values in a determinable rate. While this begins, a robust reference model and controller maintain stability of the tracking and matched parameterization error. Once the unmatched estimates have converged, the system exploits this information to switch to a more aggressive controller to guarantee global asymptotic convergence of all tracking, matched, and unmatched errors to zero. Simulations of simple aircraft dynamics demonstrate this stability and convergence.

Region-of-convergence estimation for learning-based adaptive controllers

Recent learning-based extensions to popular adaptive control procedures offer improved convergence, but at the cost of increased complexity. This complexity makes it difficult to analytically compute level sets that bound the system response. These level sets can be combined with the a priori known Lyapunov function for such systems to provide barrier certificates, verifying the safety of the system to maximum allowable error limits. This paper presents a complementary automated procedure for computing invariant level sets offline using simulation data. These level sets encompass combinations of safe initial conditions and parameters that will not cause the adaptive systems response to exceed constraints. First, conditions for the complete set of safe initial states and parameters, known as the region-of-convergence, are established. These conditions, coupled with the known Lyapunov functions describing the adaptation, are used to form an optimization procedure to construct verifiable level sets for the system response. These levels sets thus provide barrier certificates for safety and conservatively estimate the complete regionof-convergence. Lastly, the procedure is demonstrated on an adaptive control system.

Concurrent Learning Adaptive Control of the aeroelastic generic transport model

This paper presents a multiple-input Concurrent Learning Model Reference Adaptive Control (CL-MRAC) approach applied to longitudinal dynamics of the generic transport model (GTM) aircraft. A reduced order model of the short period flight dynamics coupled with structural bending and torsion is used. This aeroelastic model of the commercial passenger aircraft incorporates parametric uncertainties for mass and structural stiffness affecting both the structural dynamics and coupling. CL-MRAC with nonparametric Budgeted Kernel Restructuring (BKR) assigns centers and regressor vectors dynamically. The CL controller is used alongside an optimal tracking controller to enforce performance criteria on the rigid body dynamics. Results from this method demonstrate new insights into the application of large scale CL-MRAC implementations that arise from multiple-input multiple-output (MIMO) models.

Machine Learning for Efficient Sampling-Based Algorithms in Robust Multi-Agent Planning Under Uncertainty

Robust multi-agent planning algorithms have been developed to assign tasks to cooperative teams of robots operating under various uncertainties. Often, it is difficult to evaluate the robustness of potential task assignments analytically, so sampling-based approximations are used instead. In many applications, not only are sampling-based approximations the only solution, but these samples are computationally-burdensome to obtain. This paper presents a machine learning procedure for sampling-based approximations that actively selects samples in order to maximize the accuracy of the approximation with a limited number of samples. Gaussian process regression models are constructed from a small set of training samples and used to approximate the robustness evaluation. Active learning is then used to iteratively select samples that most improve this evaluation. Three example problems demonstrate that the new procedure achieves a similar level of accuracy as the existing sample-inefficient procedures, but with a significant reduction in the number of samples.

Output feedback concurrent learning model reference adaptive control

Concurrent learning model reference adaptive control has recently been shown to guarantee simultaneous state tracking and parameter estimation error convergence to zero without requiring the restrictive persistency of excitation condition of other adaptive methods. This simultaneous convergence drastically improves the transient performance of the adaptive system since the true model is learned, but prior results were limited to systems with full state feedback. This paper presents an output feedback form of the concurrent learning controller for a novel extension to partial state feedback systems. The approach modifies a baseline LQG/LTR adaptive law with a recorded data stack of output and state estimate vectors. This maintains the guaranteed stability and boundedness of the baseline adaptive method, while improving output tracking error response. Simulations of flexible aircraft dynamics demonstrate the improvement of the concurrent learning system over a baseline output feedback adaptive method.