In this paper we present a finite dimensional iterative algorithm for optimal maximum a posteriori (MAP) state estimation of bilinear systems. Bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems. We show that several bilinear models previously considered in the literature are special cases of the general bilinear model we propose. Our it...

f(x, y) = a x + x Qy + b y, where a, x ∈ R, b, y ∈ R, and Q is a matrix of dimension n ×m. It is easy to see that bilinear functions compose a subclass of quadratic functions. We refer to optimization problems with bilinear objective and/or constraints as bilinear problems, and they can be viewed as a subclass of quadratic programming. Bilinear programming has various applications in constraine...

The minimization control problem of quadratic functionals for the class of affine nonlinear systems with the hypothesis of nilpotent associated Lie algebra is analyzed. The optimal control corresponding to the first-, second-, and third-order nilpotent operators is determined. In this paper, we have considered the minimum fuel problem for the multi-input nilpotent control and for a scalar input...

We study the integrable discretization of coupled dispersionless equations. Two semi-discrete version and one full-discrete system are given via Hirota's bilinear method. Soliton solutions for derived discrete systems also presented.

We present a new methodology for realizing Ciphertext-Policy Attribute Encryption (CPABE) under concrete and noninteractive cryptographic assumptions in the standard model. Our solutions allow any encryptor to specify access control in terms of any access formula over the attributes in the system. In our most efficient system, ciphertext size, encryption, and decryption time scales linearly wit...

Three novel and significant contributions are made in this paper Firstly, non-recursive formulation of Haar connection coefficients, pioneered by the present authors is presented, which can be computed very efficiently and avoid stack and memory overflows. Secondly, the generalized approach for state analysis of singular bilinear time-invariant (TI) and time-varying (TV) systems is presented; v...