Systems and Control Applications

Robust and Randomized Control Design of the Mini-UAV MH1000 Platform

The results of this research have been obtained within the Italian National Project Cofin 2004 having the objective to develop a Mini-UAV platform (MH1000) for environmental monitoring, fire detection and prevention, and also natural disaster recognition. The aerial platform MH1000 is based on the MicroHawk configuration, developed at the Aerospace Engineering Department, Politecnico di Torino. The reference platform is characterized by a conventional layout consisting of fixed wing, tailless integrated wing-body configuration, tractor propeller driven. The MH1000 platform is characterized by 3.28 ft wingspan and a total weight of approximately 3.3 lb, and it was designed and tuned to meet the mission specifications required by the project. The flight envelope of the platform ranges from 20 mph to 45 mph. An average flight speed of about 34 mph allows to achieve a flight endurance of at least 40 minutes. The platform flight performance, the autopilot system effectiveness and the compliance of the integrated system to the mission requirements have been tested by extensive on-site flight tests, also in cooperation with the Environment Protection and Damage Preemption Agency of Sicily.

The reduced dimensions of the MH1000 platform lead to highly nonlinear system behavior and unconventional dynamics in terms of natural frequencies and damping ratios. The inertial characteristics of the platform yield to unconventional mode characterization thus resulting in undesirable abrupt responses to piloted commands. Furthermore, the sensitivity to changes in flight conditions (concerning velocity more than altitude), the assumptions in aerodynamic database definition (e.g., stability and control derivatives), the inaccuracies in geometric and inertial data represent a set of uncertainties in plant and environment modeling. The result is that conventional control design methods are often not effective. Therefore, the design of a robust flight control system which guarantees a suitable level of tolerance to environmental changes and platform manufacturing/modelling inaccuracies plays a key role whenever stability and performance requirements have to be fulfilled.

In this research, we developed an innovative approach for gain synthesis of the MH1000 platform which makes use of uncertainty randomization and is based on the theory of randomized algorithms. This methodology is applicable to different piloted and not piloted aircraft configurations, but it seems particularly suited for Mini-UAVs for their unconventional dynamic characteristics. The MH-1000 prototype manufacturing and a flight test of the platform are shown below.

To see pictures taken with on-board cameras (visual and infrared) click here In-flight-tests.pdf

Three randomized algorithms which should be used sequentially are presented below. The first algorithm is based upon the selection of a subset of critical uncertain parameters, and has the objective to provide an initial set of randomly generated controller gains. A specification property is considered and a stopping criterion in terms of "log-over-log" the so-called probabilistic confidence and accuracy is given. This stopping criterion is based upon the so-called Bound. Algorithm 2 uses the set of gains previously computed and evaluates the empirical probability that given performance specifications are satisfied. To this end, the Chernoff Bound is utilized. Finally, Algorithm 3 has a structure similar to Algorithm 2, but a different specification property, based on military specifications, is used.





Algorithms(1(SGS)- 2(SSRA)- 3(SPRA))

This control design methodology has been applied to the design of an embedded real-time system for autonomous flight control. The autopilot system includes guidance, navigation and loop stabilization. The obtained gain set is used for guidance/trajectory tracking and platform stabilization feedback loops. The guidance laws include altitude/velocity and heading hold loops, while the stabilization issues are related to hold attitude angles and to damp attitude rates by commanding aerodynamic control surface deflections. A plot regarding bandwidth and time delay is shown below.




Acknowledgments

This research is supported by a National Research Project Cofin (2004095094), Italian Ministry for University and Research. The aerial platform MH-1000 is based on the MicroHawk configuration, developed at the Aerospace Engineering Department, Politecnico di Torino (patent no. TO2003A000702, holder Politecnico di Torino).

References

1. L. Lorefice, B. and R. Tempo, "Randomized-Based Control Design for Mini-UVAs" Control Engineering Practice, 2009 (accepted for publication).



2. R. Tempo, G. Calafioren and F. Dabbene, "Randomized Algorithms for Analysis and Control of Uncertain Systems,"; Springer-London, 2005.



3. F.Quagliotti, G. Guglieri G.,B. Pralio and L.Lorefice","Simulation Tools for light Dynamics Analysis in the Design of MAVs", 24th ICAS Congress,Yokohama, 2004.



4. Anonymous, "Flying Qualities of Piloted Aircraft", MIL-HDBK-1797, Department of Defense, USA, 1997.

Congestion Control of High-Speed Networks

High-speed communication networks have received increasing attention in the control literature. One of the critical issues at the heart of efficient operations of high-speed networks is congestion control. This involves the problem of regulating the source rates in a decentralized and distributed fashion, so that the available bandwidths on different links are used most efficiently while minimizing or totally eliminating loss of packets due to queues at buffers exceeding their capacities. This issue needs to be accomplished under variations in network conditions such as packet delays due to propagation as well as to queueing and bottleneck nodes. Two different network topologies are shown below.




Fluid models,which replace discrete packets with continuous flows, are widely used in addressing a variety of network control problems, such as congestion control, routing and pricing. The topology of the network studied in this research is characterized by a set of nodes N and a set of links L, with each link having a fixed capacity C and an associated buffer size. Each user is associated with a unique connection between a source and a destination node. The connection is a path that connects various nodes.

In this research, simulation techniques based on randomized algorithms and, in particular, on various randomization schemes(Halton, Solbol, uniform pdf, optimal grid and Niederreiter)are explored. The results obtained provide, for example, a trade-off curve showing the network stability as a function of the link capacity.

References

1. T. Alpcan, T. Basar and R. Tempo,"Randomized Algorithms for Stability and Robustness of High-Speed Communication Networks," IEEE Transactions on Neural Networks, Vol. NN-16, pp. 1229-1241, 2005.



2. R. Tempo, G.Calafiore and F. Dabbene, "Randomized Algorithms for Analysis and Control of Uncertain Systems," Springer- Verlag, London, 2005.

Stability of Quantized and Switched Systems

We study the application of randomized algorithms to quadratic stability of sampled-data systems with memoryless quantizers. The need for quantization inevitably arises when digital networks are part of the feedback loop and it is of interest to reduce the data rate necessary for the transmission of control signals. Then, a fundamental issue is to determine the minimum information to achieve the control objectives. Clearly, if a quantized discrete-time signal takes only a finite number of fixed values, then the trajectories may go close to an equilibrium but not converge, so that asymptotic stability is not achieved. Then, various problems may be posed. For example, it is of interest to clarify how close the trajectories get to the equilibrium point and, if the sampling period is large, how close do the trajectories stay at the equilibrium between sampling instants. The structure of a quantized sampled-data system involves a plant, a quantizer Q₀, a controller K, a sampler S_T and a hold device H_T .

Based on a control Lyapunov function approach, we study quadratically attractive sets for quantized sampled-data systems. This study leads to the construction of specific randomized algorithms. The analysis method based on this approach provides a way to obtain less conservative estimates of the performance of the designed system, at the expense of obtaining a probabilistic solution instead of a guaranteed one.

Switched systems are also analyzed. In particular, we studied the construction of common Lyapunov functions for using randomized algorithms. Probabilistic and deterministic convergence are shown for infinite and finite families, respectively. Extensions to multimodal systems are considered. In this case probability-one results are obtained using a combination of randomization techniques with branch and bound methods.

References

1. H. Ishii, T.Basar and R. Tempo, "Randomized Algorithms for Synthesis of Switching Rules for Multimodal Systems", IEEE Transactions on Automatic Control, Vol. AC-50, pp. 754-767, 2005.



2. R. Tempo, G. Calafiore and F. Dabbene, "Randomized Algorithms for Analysis and Control of Uncertain Systems", Springer-Verlag, London, 2005.



3. H. Ishii, T. Basar and R. Tempo, "Randomized Algorithms for Quadratic Stability of Quantized Sampled-Data Systems",Automatica, Vol. 40, pp. 839-846, 2004.



4. D. Liberzon and R. Tempo, "Common Lyapunov Functions and Gradient Algorithms", IEEE Transactions on Automatic Control, Vol. AC-49, pp. 990-994, 2004.