• Ph.D.      TECHNION - Israel Institute of Technology (Aerospace Engineering)  2003

My posdoctoral research at UCLA focused on two main projects:

My primary area of research is in the domain of stochastic and deterministic optimal control and estimation theory with application to aerospace systems.

The various subfields of research are organized in a hierarchical way:

• Optimal Attitude Determination Algorithms: Part of the challenge is to develop efficient techniques for optimal, on-line, and autonomous processing of the information. As part of my doctoral work, novel algorithms for attitude determination using vector observations were introduced, within the general framework of linear least-squares estimation theory, with an emphasis on the representation by the quaternion of rotation. Spacecraft attitude determination from Global Positioning System (GPS) phase measurements was proposed as an application-oriented work. Future research efforts will be directed toward improved modeling and simulation of the quaternion dynamics using stochastic calculus tools and towards a further investigation of the pseudo-linear quaternion measurement model.
  
  
• Fault-Tolerant Optimal Control of Random-Switching Systems:  We are currently investigating via Dynamic Programming the Linear Quadratic Gaussian Jump problem with a random delay in the perfect and imperfection detection of the mode, both in discrete time  and in continuous time. Staying in the realm of linear least-squares estimation, we also presented suboptimal estimators of the mode for the case of full information on the continuous state. Future work is concerned with a characterization of the mode detection delay via statistical decision tools, and with the simultaneous task of optimal estimation and control of such hybrid systems, which is a dual control problem.
  
  
• Application of Optimal Estimation Theory to Non-Linear Programming: Standard optimization numerical methods, like Quasi-Newton (QN) methods, often lie at the heart of optimal control methodologies.  A challenging theoretical and practical issue consists in making the standard Quasi-Newton algorithm robust to noisy data. Preliminary results  show that the matrix filter is more robust than a standard QN algorithm for estimating the Hessian inverse matrix of the cost function in a noisy environment and that it does not loose the expanding linear manifold property in the deterministic quadratic programming case.
  
  
• Decentralized Control:
  One objective is to develop a methodology applicable to complex formations for determining the minimal information structure in some sense that ensures estimation and control. An approach that was successfully applied in a problem of fault detection and identification in a distributed system of vehicles is modified to fit the control problem. The essential difficulty is to place a measure on the desirable information; that is to design costs on the measurements according to communication constraints. The anticipated result will be a set of controllers, each choosing the information it needs for good performance.
  

My current and future research effort is organized on three different levels. At a lower level, one deals with the autonomous optimal estimation and control problem for a single
system. At a middle level, there is the issue of designing a fault-tolerant control system for each of the vehicles. At an upper level, the challenges consist in ensuring the stability and performance of the whole formation through decentralized algorithms. Although no single theory seems to evolve to embrace the totality of system complexity, a theory should emerge which provides guidance to the designer's intuition, proposes new decision architectures, and ultimately constructs nearly-optimal decision rules that coherently coordinate the multiple-vehicles platform.