Optimization for Far-distance Cooperative Rendezvous with Multiple Direction-fixed Thrusts

The continuous-thrust far-distance cooperative rendezvous problem between two spacecraft is investigated. The indirect optimization method, based on Pontryagin’s maximum principle (PMP), is applied to optimize fuel consumption. To overcome the difficulty in nonsmooth integration caused by the bang-bang control, the homotopy method is adopted to solve the fuel-optimal problem from a related energy-optimal problem. The quantum-behaved particle swarm optimization (QPSO) algorithm is used to obtain the energy-optimal solutions. The energy-optimal solutions are used as the initial values for the homotopic procedure to obtain the fuel-optimal solutions and optimal bang-bang control law. A hybrid algorithm combined homotopy method and sequential quadratic programming (SQP) algorithm is proposed. This hybrid algorithm can effectively obtain feasible optimal solutions even though the indirect optimization method exhibits a narrow convergence domain. Simulations of high-thrust and low-thrust rendezvous problems are provided and the proposed hybrid algorithm is verified. Moreover, the necessity of radial thrust is investigated.

Precise Underwater Gliders Pitch Control with the Presence of the Pycnocline

Glider-based mobile currents observations are gaining increasing research attention. However, the quality of such observations is directly related to the pitch accuracy of the glider. As a buoyancy-driven robot, the glider will be strongly disturbed during the passage through the pycnocline. The pycnocline refers to the oceanic phenomenon where the density of the seawater changes abruptly with respect to depth. The presence of the pycnocline influences the pitch of the glider and consequently affects the quality of the observed currents data. In this work, we propose an actuator constrained active disturbance rejection controller (ACADRC) to improve the accuracy of the pitch angle control when gliders move across the pycnocline. For this purpose, the dynamical model of the glider is first derived. Then, the longitudinal plane motion model of the glider considering the density variation is analyzed. Based on that, we discuss three typical types of pycnocline encountered during glider profiling, which are the pycnocline, the inverted pycnocline and the multiple pycnocline. To alleviate the low accuracy of bang-bang control and proportion integration differentiation control, and furthermore, to mitigate the disturbance of pitch by sudden density changes, we propose the actuator constrained active disturbance rejection controller in conjunction with specific glider pitch actuator hardware constraints. Simulation results show that the proposed method has significant improvement in pitch control accuracy over the comparison methods.

Nonlinear dynamics and control of helicopter ground resonance

Ground resonance is an aero-mechanical instability in helicopters that use soft in-plane rotors. Traditionally, ground resonance is mitigated by using passive lead–lag dampers that provide sufficient in-plane damping. However, these dampers because of their passive nature cannot adapt to all operating conditions. In this work, a magnetorheological fluid–based semi-active lead–lag damper is proposed to offer controllable damping. Two nonlinear control strategies are reported to operate the voltage to be supplied to the magnetorheological damper. The first strategy is a model-based control using dynamic inversion. The second is a fuzzy logic control integrated with a particle swarm optimization algorithm to optimize the control parameters. Both control strategies are shown to be effective in eliminating ground resonance. Unlike bang–bang control, the prescribed control algorithms can make use of complete voltage level available in the magnetorheological damper with smooth voltage updates. A comparative study of the controller performances is made through appropriate performance indices and system responses. Finally, the most optimum control strategy to mitigate ground resonance is inferred.

An Optimal Control Study with Quantity of Additional food as Control in Prey-Predator Systems involving Inhibitory Effect

Additional food provided prey-predator systems have become a significant and important area of study for both theoretical and experimental ecologists. This is mainly because provision of additional food to the predator in the prey-predator systems has proven to facilitate wildlife conservation as well as reduction of pesticides in agriculture. Further, the mathematical modeling and analysis of these systems provide the eco-manager with various strategies that can be implemented on field to achieve the desired objectives. The outcomes of many theoretical and mathematical studies of such additional food systems have shown that the quality and quantity of additional food play a crucial role in driving the system to the desired state. However, one of the limitations of these studies is that they are asymptotic in nature, where the desired state is reached eventually with time. To overcome these limitations, we present a time optimal control study for an additional food provided prey-predator system involving inhibitory effect with quantity of additional food as the control parameter with the objective of reaching the desired state in finite (minimum) time. The results show that the optimal solution is a bang-bang control with a possibility of multiple switches. Numerical examples illustrate the theoretical findings. These results can be applied to both biological conservation and pest eradication.