Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming

There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these systems is challenging due to the nonlinear and compositional structure of neural networks. In this paper, we propose a novel forward reachability analysis method for the safety verification of linear time-varying systems with neural networks in feedback interconnection. Our technical approach relies on abstracting the nonlinear activation functions by quadratic constraints, which leads to an outer-approximation of forward reachable sets of the closed-loop system. We show that we can compute these approximate reachable sets using semidefinite programming. We illustrate our method in a quadrotor example, in which we first approximate a nonlinear model predictive controller via a deep neural network and then apply our analysis tool to certify finite-time reachability and constraint satisfaction of the closed-loop system

Efficient Control of DC Servomotor Systems Using Backpropagation Neural Networks

DC motor systems have played an important role in the improvement and development of the industrial revolution, making them the heart of different applications beside AC motor systems. Therefore, the development of a more efficient control strategy that can be used for the control of a DC servomotor system, and a well defined mathematical model that can be used for off line simulation are essential for this type of systems Servomotor systems are known to have nonlinear parameters and dynamic factors, such as backlash, dead zone and Coulomb friction that make the systems hard to control using conventional control methods such as PID controllers. Also, the dynamics of the servomotor and outside factors add more complexity to the analysis of the system, for example when the load attached to the control system changes. Due to these parameters and factors new intelligent control techniques such as Neural Networks, genetic algorithms and Fuzzy logic methods are under research consideration in order to solve the complex problems related to the control of these nonlinear systems. In this research we are using a combination of two multilayer neural networks to implement the control system: a) The first network is used to build a model that mimics the function of DC servomotor system, and b) a second network is used to implement the controller that controls the operation of the model network using backpropagation learning technique. The proposed combination of the two neural networks will be able to deal with the nonlinear parameters and dynamic factors involved in the original servomotor system and hence generate the proper control of the output speed and position. Off line simulation using MATLAB Neural Network toolbox is used to show final results, and to compare them with a conventional PID controller results for the same model

Trajectory Tracking Error Using Fractional Order PID Control Law for Two‐Link Robot Manipulator via Fractional Adaptive Neural Networks

The problem of trajectory tracking of unknown nonlinear systems of fractional order is solved using fractional order dynamical neural networks. For this purpose, we obtained control laws and laws of adaptive weights online, obtained using the Lyapunov stability analysis methodology of fractional order. Numerical simulations illustrate the obtained theoretical results

Neural network application to aircraft control system design

The feasibility of using artificial neural networks as control systems for modern, complex aerospace vehicles is investigated via an example aircraft control design study. The problem considered is that of designing a controller for an integrated airframe/propulsion longitudinal dynamics model of a modern fighter aircraft to provide independent control of pitch rate and airspeed responses to pilot command inputs. An explicit model following controller using H infinity control design techniques is first designed to gain insight into the control problem as well as to provide a baseline for evaluation of the neurocontroller. Using the model of the desired dynamics as a command generator, a multilayer feedforward neural network is trained to control the vehicle model within the physical limitations of the actuator dynamics. This is achieved by minimizing an objective function which is a weighted sum of tracking errors and control input commands and rates. To gain insight in the neurocontrol, linearized representations of the nonlinear neurocontroller are analyzed along a commanded trajectory. Linear robustness analysis tools are then applied to the linearized neurocontroller models and to the baseline H infinity based controller. Future areas of research are identified to enhance the practical applicability of neural networks to flight control design

Discrete Globalised Dual Heuristic Dynamic Programming in Control of the Two-Wheeled Mobile Robot

Network-based control systems have been emerging technologies in the control of nonlinear systems over the past few years. This paper focuses on the implementation of the approximate dynamic programming algorithm in the network-based tracking control system of the two-wheeled mobile robot, Pioneer 2-DX. The proposed discrete tracking control system consists of the globalised dual heuristic dynamic programming algorithm, the PD controller, the supervisory term, and an additional control signal. The structure of the supervisory term derives from the stability analysis realised using the Lyapunov stability theorem. The globalised dual heuristic dynamic programming algorithm consists of two structures: the actor and the critic, realised in a form of neural networks. The actor generates the suboptimal control law, while the critic evaluates the realised control strategy by approximation of value function from the Bellman’s equation. The presented discrete tracking control system works online, the neural networks’ weights adaptation process is realised in every iteration step, and the neural networks preliminary learning procedure is not required. The performance of the proposed control system was verified by a series of computer simulations and experiments realised using the wheeled mobile robot Pioneer 2-DX

Neural networks in feedback for flow analysis, sensor placement and control

This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the Kuramoto-Sivashinsky equation, a streamwise-periodic 2D channel flow, and a confined cylinder flow. Neural networks are trained as models to capture the complex system dynamics and estimate equilibrium points through a Newton method, enabled by backpropagation. These neural network surrogate models (NNSMs) are leveraged to train a second neural network, which is designed to act as a stabilizing closed-loop controller. The training process employs a recurrent approach, whereby the NNSM and the neural network controller (NNC) are chained in closed loop along a finite time horizon. By cycling through phases of combined random open-loop actuation and closed-loop control, an iterative training process is introduced to overcome the lack of data near equilibrium points. This approach improves the accuracy of the models in the most critical region for achieving stabilization. Through the use of L1 regularization within loss functions, the NNSMs can also guide optimal sensor placement, reducing the number of sensors from an initial candidate set. The datasets produced during the iterative training process are also leveraged for conducting a linear stability analysis through a modified dynamic mode decomposition approach. The results demonstrate the effectiveness of computationally inexpensive neural networks in modeling, controlling, and enabling stability analysis of nonlinear systems, providing insights into the system behaviour and offering potential for stabilization of complex fluid systems.Comment: 30 pages, 22 figures, under consideration for publicatio

Using feedforward neural networks to represent ecosystem dynamics for bioeconomic analysis

We applied feedforward neural networks to represent ecosystem dynamics that are vital to bioeconomic analysis, ecosystem-based management, or what-if analysis regarding the underlying natural resources. Neural networks are flexible, universal function approximators, recognized for their ability to recover complex nonlinear relationships. In this paper, we treated outputs from an end-to-end Atlantis model as synthetic data and used them as training data for the neural networks. After learning the seasonal dynamics of a multispecies system, we forecasted system states with different sets of specified harvest policies using the trained networks. We demonstrate that neural networks can capture key dynamics in part of the ecosystem efficiently, and give fast updates of states that are needed for optimization and decision-making. The trained networks are reduced and more flexible systems compared to the large-scale simulator model, which is more costly to run and does not have a format allowing human actions in the form of feedback policies, or harvest control rules, i.e. decisions depending on states as well as time.publishedVersio

Value iteration with deep neural networks for optimal control of input-affine nonlinear systems

This paper proposes a new algorithm with deep neural networks to solve optimal control problems for continuous-time input nonlinear systems based on a value iteration algorithm. The proposed algorithm applies the networks to approximating the value functions and control inputs in the iterations. Consequently, the partial differential equations of the original algorithm reduce to the optimization problems for the parameters of the networks. Although the conventional algorithm can obtain the optimal control with iterative computations, each of the computations needs to be completed precisely, and it is hard to achieve sufficient precision in practice. Instead, the proposed method provides a practical method using deep neural networks and overcomes the difficulty based on a property of the networks, under which our convergence analysis shows that the proposed algorithm can achieve the minimum of the value function and the corresponding optimal controller. The effectiveness of the proposed method even with reasonable computational resources is demonstrated in two numerical simulations