Bayesian Nonparametric Adaptive Control using Gaussian Processes

This technical report is a preprint of an article submitted to a journal.Most current Model Reference Adaptive Control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element are Radial Basis Function Networks (RBFNs), with RBF centers pre-allocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become non-effective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semi-global in nature. This paper investigates a Gaussian Process (GP) based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.This research was supported in part by ONR MURI Grant N000141110688 and NSF grant ECS #0846750

Composite learning adaptive backstepping control using neural networks with compact supports

© 2019 John Wiley & Sons, Ltd. The ability to learn is crucial for neural network (NN) control as it is able to enhance the overall stability and robustness of control systems. In this study, a composite learning control strategy is proposed for a class of strict-feedback nonlinear systems with mismatched uncertainties, where raised-cosine radial basis function NNs with compact supports are applied to approximate system uncertainties. Both online historical data and instantaneous data are utilized to update NN weights. Practical exponential stability of the closed-loop system is established under a weak excitation condition termed interval excitation. The proposed approach ensures fast parameter convergence, implying an exact estimation of plant uncertainties, without the trajectory of NN inputs being recurrent and the time derivation of plant states. The raised-cosine radial basis function NNs applied not only reduces computational cost but also facilitates the exact determination of a subregressor activated along any trajectory of NN inputs so that the interval excitation condition is verifiable. Numerical results have verified validity and superiority of the proposed approach

Real-Time Progressive Learning: Mutually Reinforcing Learning and Control with Neural-Network-Based Selective Memory

Memory, as the basis of learning, determines the storage, update and forgetting of the knowledge and further determines the efficiency of learning. Featured with a mechanism of memory, a radial basis function neural network (RBFNN) based learning control scheme named real-time progressive learning (RTPL) is proposed to learn the unknown dynamics of the system with guaranteed stability and closed-loop performance. Instead of the stochastic gradient descent (SGD) update law in adaptive neural control (ANC), RTPL adopts the selective memory recursive least squares (SMRLS) algorithm to update the weights of the RBFNN. Through SMRLS, the approximation capabilities of the RBFNN are uniformly distributed over the feature space and thus the passive knowledge forgetting phenomenon of SGD method is suppressed. Subsequently, RTPL achieves the following merits over the classical ANC: 1) guaranteed learning capability under low-level persistent excitation (PE), 2) improved learning performance (learning speed, accuracy and generalization capability), and 3) low gain requirement ensuring robustness of RTPL in practical applications. Moreover, the RTPL based learning and control will gradually reinforce each other during the task execution, making it appropriate for long-term learning control tasks. As an example, RTPL is used to address the tracking control problem of a class of nonlinear systems with RBFNN being an adaptive feedforward controller. Corresponding theoretical analysis and simulation studies demonstrate the effectiveness of RTPL.Comment: 16 pages, 15 figure

Adapt-to-learn policy transfer in reinforcement learning and deep model reference adaptive control

Adaptation and Learning from exploration have been a key in biological learning; Humans and animals do not learn every task in isolation; rather are able to quickly adapt the learned behaviors between similar tasks and learn new skills when presented with new situations. Inspired by this, adaptation has been an important direction of research in control as Adaptive Controllers. However, the Adaptive Controllers like Model Reference Adaptive Controller are mainly model-based controllers and do not rely on exploration instead make informed decisions exploiting the model's structure. Therefore such controllers are characterized by high sample efficiency and stability conditions and, therefore, suitable for safety-critical systems. On the other hand, we have Learning-based optimal control algorithms like Reinforcement Learning. Reinforcement learning is a trial and error method, where an agent explores the environment by taking random action and maximizing the likelihood of those particular actions that result in a higher return. However, these exploration techniques are expected to fail many times before exploring optimal policy. Therefore, they are highly sample-expensive and lack stability guarantees and hence not suitable for safety-critical systems. This thesis presents control algorithms for robotics where the best of both worlds that is ``Adaptation'' and ``Learning from exploration'' are brought together to propose new algorithms that can perform better than their conventional counterparts. In this effort, we first present an Adapt to learn policy transfer Algorithm, where we use control theoretical ideas of adaptation to transfer policy between two related but different tasks using the policy gradient method of reinforcement learning. Efficient and robust policy transfer remains a key challenge in reinforcement learning. Policy transfer through warm initialization, imitation, or interacting over a large set of agents with randomized instances, have been commonly applied to solve a variety of Reinforcement Learning (RL) tasks. However, this is far from how behavior transfer happens in the biological world: Here, we seek to answer the question: Will learning to combine adaptation reward with environmental reward lead to a more efficient transfer of policies between domains? We introduce a principled mechanism that can ``Adapt-to-Learn", which is adapt the source policy to learn to solve a target task with significant transition differences and uncertainties. Through theory and experiments, we show that our method leads to a significantly reduced sample complexity of transferring the policies between the tasks. In the second part of this thesis, information-enabled learning-based adaptive controllers like ``Gaussian Process adaptive controller using Model Reference Generative Network'' (GP-MRGeN), ``Deep Model Reference Adaptive Controller'' (DMRAC) are presented. Model reference adaptive control (MRAC) is a widely studied adaptive control methodology that aims to ensure that a nonlinear plant with significant model uncertainty behaves like a chosen reference model. MRAC methods try to adapt the system to changes by representing the system uncertainties as weighted combinations of known nonlinear functions and using weight update law that ensures that network weights are moved in the direction of minimizing the instantaneous tracking error. However, most MRAC adaptive controllers use a shallow network and only the instantaneous data for adaptation, restricting their representation capability and limiting their performance under fast-changing uncertainties and faults in the system. In this thesis, we propose a Gaussian process based adaptive controller called GP-MRGeN. We present a new approach to the online supervised training of GP models using a new architecture termed as Model Reference Generative Network (MRGeN). Our architecture is very loosely inspired by the recent success of generative neural network models. Nevertheless, our contributions ensure that the inclusion of such a model in closed-loop control does not affect the stability properties. The GP-MRGeN controller, through using a generative network, is capable of achieving higher adaptation rates without losing robustness properties of the controller, hence suitable for mitigating faults in fast-evolving systems. Further, in this thesis, we present a new neuroadaptive architecture: Deep Neural Network-based Model Reference Adaptive Control. This architecture utilizes deep neural network representations for modeling significant nonlinearities while marrying it with the boundedness guarantees that characterize MRAC based controllers. We demonstrate through simulations and analysis that DMRAC can subsume previously studied learning-based MRAC methods, such as concurrent learning and GP-MRAC. This makes DMRAC a highly powerful architecture for high-performance control of nonlinear systems with long-term learning properties. Theoretical proofs of the controller generalizing capability over unseen data points and boundedness properties of the tracking error are also presented. Experiments with the quadrotor vehicle demonstrate the controller performance in achieving reference model tracking in the presence of significant matched uncertainties. A software+communication architecture is designed to ensure online real-time inference of the deep network on a high-bandwidth computation-limited platform to achieve these results. These results demonstrate the efficacy of deep networks for high bandwidth closed-loop attitude control of unstable and nonlinear robots operating in adverse situations. We expect that this work will benefit other closed-loop deep-learning control architectures for robotics