We look at the situation of controlling a poorly known system, for which only a simplified and uncertain model can be used for control design purposes. This setting is commonly found in biological systems or economic policy-making. We employ the idea of the CVIU approach [1], and develop in the scalar case the solution of the HJB equation. The control design is compared with the standard and robust LQG solutions, exploring the fact that the model can be quite distinct of the actual system.We verify that in some mismatched situations the CVIU approach yields better performance than the LQG strategies. © 2013 IEEE. 18861891et al.,Honeywell,MathWorks,Springer,Taylor and Francis Group,University of TriesteSouto, R.F., Val, J.B.R.D., A stochastic model to account for system uncertainties applied to an optimal harvesting problem (2012) Proc. 7th IFAC Symposium on Robust Control Design, pp. 39-44. , Aalborg, Denmark, JuneZhou, K., Doyle, J.C., Glover, K., (1996) Robust and Optimal Control, , Prentice Hall, New JerseyCalmon, A.P., Valle, T., Do Val, J.B.R., Control variation as a source of uncertainty: Single input case (2009) Proc. American Control Conference, pp. 4416-4421. , St. Louis, MO, USA, JuneSouto, R.F., Do Val, J.B.R., Underdetermined stochastic systems modelled by a control dependent diffusion (2012) Proc. 10th Portuguese Conference on Automatic Control, pp. 167-172. , Funchal, Madeira Island, JulyOksendal, B., (2007) Stochastic Differential Equations - An Introduction with Applications, , Springer, BlindernBoyd, S., Vandenberghe, L., (2004) Convex Optimization, , Cambridge University PressClarke, F.H., (1987) Optimization and Nonsmooth Analysis, , Society for Industrial and Applied MathematicsBoyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , Philadelphia, PA: SIAM Studies in Applied MathematicsGeromel, J.C., Peres, P.L.D., Souza, S.R., H2 guaranteed cost control for uncertain continuous-time linear systems (1992) Systems & Control Letters, 19 (1), pp. 23-27. , JulyLöfberg, J., YALMIP: A toolbox for modeling and optimization in matlab (2004) Proc. 2004 IEEE Int. Symp. on Comput. Aided Control Syst. Des., pp. 284-289. , http://control.ee.ethz.ch/joloef/yalmip.php, Taipei, Taiwan, SeptemberSturm, J.F., Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones (1999) Optim. Method Softw., 11 (1-4), pp. 625-653. , http://sedumi.ie.lehigh.edu/