11,234 research outputs found
Motion Planning of Uncertain Ordinary Differential Equation Systems
This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems.
Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs.
The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space
Random Neural Networks and Optimisation
In this thesis we introduce new models and learning algorithms for the Random
Neural Network (RNN), and we develop RNN-based and other approaches for the
solution of emergency management optimisation problems.
With respect to RNN developments, two novel supervised learning algorithms are
proposed. The first, is a gradient descent algorithm for an RNN extension model
that we have introduced, the RNN with synchronised interactions (RNNSI), which
was inspired from the synchronised firing activity observed in brain neural circuits.
The second algorithm is based on modelling the signal-flow equations in RNN as a
nonnegative least squares (NNLS) problem. NNLS is solved using a limited-memory
quasi-Newton algorithm specifically designed for the RNN case.
Regarding the investigation of emergency management optimisation problems,
we examine combinatorial assignment problems that require fast, distributed and
close to optimal solution, under information uncertainty. We consider three different
problems with the above characteristics associated with the assignment of
emergency units to incidents with injured civilians (AEUI), the assignment of assets
to tasks under execution uncertainty (ATAU), and the deployment of a robotic
network to establish communication with trapped civilians (DRNCTC).
AEUI is solved by training an RNN tool with instances of the optimisation problem
and then using the trained RNN for decision making; training is achieved using
the developed learning algorithms. For the solution of ATAU problem, we introduce
two different approaches. The first is based on mapping parameters of the
optimisation problem to RNN parameters, and the second on solving a sequence of
minimum cost flow problems on appropriately constructed networks with estimated
arc costs. For the exact solution of DRNCTC problem, we develop a mixed-integer
linear programming formulation, which is based on network flows. Finally, we design
and implement distributed heuristic algorithms for the deployment of robots
when the civilian locations are known or uncertain
Validation of Neural Network Controllers for Uncertain Systems Through Keep-Close Approach: Robustness Analysis and Safety Verification
Among the major challenges in neural control system technology is the
validation and certification of the safety and robustness of neural network
(NN) controllers against various uncertainties including unmodelled dynamics,
non-linearities, and time delays. One way in providing such validation
guarantees is to maintain the closed-loop system output with a NN controller
when its input changes within a bounded set, close to the output of a robustly
performing closed-loop reference model. This paper presents a novel approach to
analysing the performance and robustness of uncertain feedback systems with NN
controllers. Due to the complexity of analysing such systems, the problem is
reformulated as the problem of dynamical tracking errors between the
closed-loop system with a neural controller and an ideal closed-loop reference
model. Then, the approximation of the controller error is characterised by
adopting the differential mean value theorem (DMV) and the Integral Quadratic
Constraints (IQCs) technique. Moreover, the Relative Integral Square Error
(RISE) and the Supreme Square Error (SSE) bounded set are derived for the
output of the error dynamical system. The analysis is then performed by
integrating Lyapunov theory with the IQCs-based technique. The resulting
worst-case analysis provides the user a prior knowledge about the worst case of
RISE and SSE between the reference closed-loop model and the uncertain system
controlled by the neural controller. The suitability of the proposed technique
is demonstrated by the results obtained on a nonlinear single-link robot system
with a NN trained to control the movement of this mechanical system while
keeping close to an ideal closed-loop reference model.Comment: 19 pages, 10 figures, Journal Paper submitted to IEEE Transactions on
Control Systems Technolog
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